Physics
Integrated Ph D Programme
Physical Sciences
Departmental Core
Hard Core: 45
Credits (all courses are compulsory)
Course Credits
Course Title
PH 201 3:0 Classical
Mechanics
PH 202 3:0 Statistical
Mechanics
PH 203 3:0 Quantum
Mechanics I
PH 204 3:0 Quantum
Mechanics II
PH 205 3:0 Mathematical
Methods of
Physics
PH 206 3:0 Electromagnetic Theory
PH 207 1:2 Analog Digital and
Microprocessor Electronics
PH 208 3:0 Condensed Matter Physics-I
PH 209 2:1 Analog and Digital Electronics
Lab
PH 211 0:3 General Physics Laboratory
PH 212 0:3 Experiments in Condensed
Matter Physics
PH 213 0:4 Advanced Experiments in
Condensed Matter Physics
PH 215/
HE 215 3:0 Nuclear and Particle Physics
PH 217 3:0 Fundamentals of Astrophysics
PH 231 0:1 Workshop practice
PH 300 1:0 Seminar Course
Project:
PH 250A 0:6 Project
PH 250B 0:6 Project
List of Elective
Courses:
PH 316/
HE 316 3:0 Advanced Mathematical
Methods
PH 320 3:0 Condensed Matter Physics II
PH 322 3:0 Molecular Simulation
PH 325 3:0 Advanced Statistical Physics
PH 326 3:0 Principles & Techniques of
Magnetic Resonance I
PH 327 3:0 Principles & Techniques of
Magnetic Resonance II
PH 330 0:3 Advanced Independent Project
in Physics
PH 347 2:0 Bioinformatics
PH 350 3:0 Physics of Soft Condensed
Matter
PH 351 2:0
Characterization
PH 352 3:0 Semiconductor
Physics and
Technology
PH 353 3:0 Principles of
Magnetism in
Solids
PH 359 3:0 Physics at
the Nanoscale
PH 360 3:0 Biological
Physics
PH 340 4:0 Quantum Statistical Field
Theory
HE 392/
PH 392 3:0 Standard Model of Particle
Physics
PH 395/
HE 395 3:0 Quantum Mechanics III
PH 396/
HE 396 3:0 Gauge Field Theories
PH 201 (AUG) 3:0
Classical
Mechanics
Vasant Natarajan and K P Ramesh
Goldstein, H., Classical
Mechanics, Second Edn, Narosa,
Landau,
L.D., and Lifshitz, E.M., Mechanics,
PH 202 (JAN) 3:0
Statistical
Mechanics
Basic
principles of statistical mechanics and its application to a few simple
systems. Probability theory, fundamental
postulate, phase space, Liouville’s theorem, ergodicity, microcanical
ensemble, connection with thermodynamics, canonical ensemble, classical ideal
gas, harmonic oscillators, paramagnetism, Ising model, physical applications to polymers, biophysics.
Grand canonical ensemble, thermodynamic potentials, Maxwell relations, Legendre
transformation, introduction to quantum statistical mechanics, Fermi, Bose and
Boltzmann distribution, Bose condensation, photons and phonons, Fermi gas,
classical gases with internal degrees of freedom, fluctuation, dissipation and
linear response, Monte Carlo and molecular dynamics methods.
H
R Krishnamurthy
Pathria, R.K., Statistical Mechanics, Butterworth Heinemann, Second Edn, 1996.
Reif, F.,
Fundamentals of Statistical and thermal Physics, McGraw Hill, 1965.
Huang,
K., Statistical Mechanics,
Bhattacharjee, J.K., Statistical Mechanics: Equilibrium and
non-equilibrium aspects.
J P Sethna,
J.P., Statistical Mechanics: Entropy, Order Parameters and Complexity,
PH 203 (AUG) 3:0
Quantum
Mechanics-I
Examples
of probability amplitudes and superposition. Preparation, measu-rement, and evolution
of states in a two level systems, e.g polarised light, Stern Gerlach
experiments. Matrix formulation of quantum theory.
Unitary and Hermitean operators and
the properties. Wave functions for a single particle. Momentum
operator and representation. Time evolution, the
Hamiltonian, Schrodinger equation. Probability current, wave packets,
uncertainty principle, classical limit. Stationary states,
their orthogonality and completeness. Variational
methods. One dimensional problems – bound
states, tunneling, scattering. The harmonic oscillator, analytical and operator
approaches. Three dimensional problems. Symmetries, conservation laws, degeneracies,
with examples. Infinitesimal rotations, angular
momentum operators, commutation relations and their consequences. Separation of variables for a central force problem. Spherical harmonics. The hydrogen atom.
Alkali atoms. The spin orbit and hyperfine
interactions. Time independent perturbation theory,
non-degenerate and degenerate cases. Fine and
hyperfine structure of energy levels. Stark and Zeeman
effects.
Sriram Ramaswamy
Cohen-Tannoudji, C.,
Merzbacher, E., Quantum
Mechanics, John Wiley & Sons, 1968.
Thankappon, V.K., Quantum Mechanics, Wiley Eastern Ltd., 1993.
PH 204 (JAN) 3:0
Quantum
Mechanics II
Time
dependent perturbation theory. Fermi
golden rule. Transitions caused by a periodic external field. Dipole transitions and selection rules. Decay of an unstable
state. Born cross section for weak potential scattering.
Adiabatic and sudden approximations. WKB method for bound states and tunneling. Scattering theory: partial wave analysis, low energy scattering,
scattering length, born approximation, optical theorem, Levinson’s theorem,
resonances, elements of formal scattering theory. Minimal
coupling between radiation and matter, diamagnetism and paramagnetism
of atoms, Landau levels and Aharonov Bohm effect. Addition of angular momenta, Clebsch Gordon series,
Wigner Eckart theorem, Lande’s
g factor. Many particle systems: identity of particles, Pauli principle,
exchange interaction, bosons and fermions. Second
quantization, multielectron atoms, Hund’s rules. Binding of diatomic
molecules. Introduction to Klein Gordon and Dirac
equations, and their non relativistic reduction, g factor of the electron.
Chandan Dasgupta
Landau,
L.D., and Lifshitz E.M., Quantum Mechanics,
Baym, G., Lectures on Quantum Mechanics,
Bethe,
H.A., and Jackiw, R., Intermediate Quantum Mechanics,
PH 205 (AUG) 3:0
Mathematical
Methods of Physics
Linear
vector spaces, linear operators and matrices, systems of linear equations. Eigen values and eigen
vectors, classical orthogonal polynomials. Linear ordinary
differential equations, exact and series methods of solution, special
functions. Linear partial differential equations of
physics, separation of variables method of solution. Complex
variable theory; analytic functions. Taylor and
Laurent expansions, classification of singularities, analytic continuation,
contour integration, dispersion relations. Fourier and Laplace
transforms.
Diptiman Sen
Mathews, J., and
Dennery, P., and
Krzywicki, A., Mathematics for Physicists, Harper and
Row, NY, 1967.
Wyld, H.W., Mathematical
Methods for Physics, Benjam,
PH 206 (JAN) 3:0
Electromagnetic
Theory
Laws of electrostatics
and methods of solving boundary value problems. Multipole expansion of
electrostatic potentials, spherical harmonics. Electostatics in material media,
dielectrics. Biot-Savart Law, magnetic field and the vector potential. Faraday’s Law
and time varying fields. Maxwell’s equations, energy and
momentum of the electromagnetic field, Poynting
vector, conservation laws. Propagation of plane
electromagnetic waves. Radiation from an accelerated charge,
retarded and advanced potentials, Lienard-Wiechert
potentials, radiation multipoles. Special
theory of relativity and its application in electromagnetic theory.
Maxwell’s equations in covariant form: four – potentials, electromagnetic field
tensor, field Lagrangian. Elements
of classical field theory, gauge invariance in electromagnetic theory.
Arnab Rai Choudhuri
Jackson, J.D., Classical
Electrodynamics, Third Edn, John Wiley.
Panofsky,
W.K.H., and Phillips, M., Classical Electricity and Magnetism, Second Edn,
PH 207 (JAN) 1:2
Electronics
– I
Basic diode and
transistor circuits, operational amplifier and applications, active filters,
voltage regulators, oscillators, digital electronics, logic gates, Boolean
algebra, flip-flops, multiplexers, counters, displays, decoders, D/A, A/D.
Introduction to microprocessors.
V
Venkataraman
Horowitz
and Hill, The Art of Electronics, Second Edn.
Millman and Halkias, Integrated Electronics, McGraw Hill.
Gayakwad, R., Operational
amplifiers and Linear Integrated Circuits.Publishers?
PH 208 (JAN) 3:0
Condensed
Matter Physics I
Drude model, Sommerfeld model, crystal lattices,
reciprocal lattice, x-ray diffraction, Brillouin
zones and Fermi surfaces, Bloch’s theorem, nearly free electrons, tight binding
model, selected band structures, semiclassical
dynamics of electrons, measuring Fermi surfaces, cohesive energy, classical
harmonic crystal, quantum harmonic crystal, phonons in
metals, semiconductors, diamagnetism and paramagnetism,
magnetic interactions.
Arindam Ghosh
Ashcroft,
N.W., and
Kittel, C.,
Introduction to Solid State Physics, 5th/6th/7th editions, Wiley International,
PH 209 (AUG) 2:1
Analog and
Digital Electronics Laboratory
Introduction to microprocessors,
Intel 80x86 architecture, instruction set. Assembly
and C level programming, memory and IO interfacing. Mini projects using
integrated circuits, Data acquisition systems. PC Add-on boards. Introduction to Virtual Instrumentation.
K Rajan and K
Hall, DV.,
Digital circuits and systems, McGraw Hill International Electronic
Engineering Series.
Hall, DV.,
Microprocessors and Interfacing, Second Edn, Tata
McGraw Hill.
Robert Bishop, Learning with LabView Express, Pearson Edn.
PH 211 (AUG) 0:3
General
Physics Laboratory
Diffraction of light by
high frequency sound waves, Michelson interferometer, Hall effect, band gap of
semiconductors, diode as a temperature sensor, thermal conductivity of a gas
using Pirani gauge, normal modes of vibration in a
box, Newton’s laws of cooling, dielectric constant measurements of triglycine selenate, random walk
in porous medium.
Vasant Natarajan, K P Ramesh and Prasad V Bhotla
PH 212 (JAN) 0:3
Experiments
in Condensed Matter Physics
Hall coefficient carrier
mobility and life-time in semiconductors, resistivity measurement in
anisotropic materials, crystal growth, crystal optics, light scattering,
electron tunnelling, resonance spectroscopy, coexistence curve for binary liquid mixtures, magnetic
susceptibility, dielectric loss and dispersion. Meissner
fraction of a high temperature superconductor, the specific heat of a glass,
microwave and rf absorption in high Tc materials, surface studies by STM in air, electron
tunneling/STM magnetic susceptibility, calibration of a cryogenic temperature
sensor (oxide/Ge sensor), resistivity vs temperature of a superconductor.
Reghu Menon, Suja Elizabeth and D V
Weider, Lab. notes of electrical measurements.
Smith and Richardson, Experimental methods in low
temperature physics.
PH 213 (AUG) 0:4
Advanced
Experiments in Condensed Matter Physics
This
lab course has two components: In the first part, the students will do the
following five experiments in the Central Instruments Facility of the
department to learn about the basic preparation characterization tools.
1.
Laue diffraction
2.
Powder diffraction
3.
Differential Scanning calorimetry
4.
Optical absorption spectra
5.
RF sputtering
In
the second part the students will do an 8 weeks project in a designated lab
under the supervision of a faculty member. Such projects will be floated at the
beginning of the semester and students will have to choose from among the
available projects.
Ramesh C Mallik, Prasad V Bhotla and V. Venkataraman
HE 215 / PH 215 (AUG) 3:0
Nuclear
and Particle Physics
Radioactive
decay, subnuclear particles. Binding energies. Nuclear forces, pion exchange, Yukawa potential. Isospin, neutron and proton.
Deuteron. Shell model, magic numbers. Nuclear transitions. Selection rules.
Liquid drop model. Collective
excitations. Nuclear fission and fusion. Beta decay. Neutrinos. Fermi theory, parity violation, V-A theory. Mesons and baryons. Lifetimes and decay processes. Discrete
symmetries, C, P, T and G. Weak interaction transition rules. Strangeness, K mesons and hyperons. Composition
of mesons and baryons, quarks and gluons.
B
Ananthanarayan
Povh, B., Rith, K., Scholz,
C., and Zetsche, F., Particles and Nuclei, An
Introduction to Physical Concepts, Second Edn,
Springer, 1999.
Krane, K.S.,
Introductory Nuclear Physics, John Wiley and Sons, NY, 1988.
Perkins, D.H.,
Introduction to High Energy Physics, Third edition, Addison-Wesley,
PH 217 (AUG) 3:0
Fundamentals
of Astrophysics
Overview
of the major contents of the universe. Basics of radiative transfer and radiative processes. Stellar
interiors. HR diagram. Nuclear
energy generation. White dwarfs and neutron stars.
Shape, size and contents of our galaxy. Basics of stellar dynamics. Normal and
active galaxies. High energy and plasma processes. Newtonian
cosmology. Microwave background. Early universe.
B
Mukhopadhyay
Choudhuri,
A.R., Astrophysics for Physicists
Shu,
F., The Physical Universe.
Shapiro,
S.L., and
Carroll,
B.W., and Ostlie, D.A., Introduction to Modern
Astrophysics.
PH 231 (AUG) 0:1
Workshop
practice
Use of lathe, milling
machine, drilling machine, and elementary carpentry Working
with metals such as brass, aluminium and steel.
K
PH 250A (JAN) 0:6
Project
– I
PH 250B (MAY) 0:6
Project
– II
This two part project is
offered by the faculty members of the department. It starts in the fourth
semester of the Integrated Ph.D Programme
(PH 250 A) and ends in the summer before the beginning of the 5th semester (PH
250B).
PH 300 (AUG) 1:0
Seminar
Course
The course aims to help
the fresh research student in preparing, presenting and participating in
seminars. These seminars are run in a course form after proper guidance by the
instructors, They will be given by the students who
register for this course.
Vijay
Shenoy and Arindam Ghosh
HE 316 / PH 316 (JAN) 3:0
Advanced
Mathematical Methods
Introduction
to finite and continuous groups. Group representations and operations on them. Permutation group and its representations. Lie groups and
Lie algebras. SU(2), SU(3) and SU(N) groups. Roots and weights. Lorentz and Poincare
groups. Introduction to manifolds, differential geometry, fibre bundles, topology and homotopy.
Aninda Sinha
Hamermesh, M.,
Group Theory and its Applications to Physical Problems, Addison-Wesley,
Mukhi, S., and Mukunda, N., Introduction to Topology, Differential
Geometry and Group Theory for Physicists, Wiley Eastern, 1990.
Nash,
C., and Sen, S., Topology and geometry for physicists,
Academic Press, 1988.
Schutz, B. F., Geometrical Methods of Mathematical Physics,
PH 320 (AUG) 3:0
Condensed
Matter Physics - II
Review of one-electron
band theory. Effects of electron-electron interaction: Hartree
– Fock approximation, exchange and correlation
effects, density functional theory, Fermi liquid theory, elementary
excitations, quasiparticles. Dielectric
function of electron systems, screening, plasma oscillation. Optical properties of metals and insulators, excitons.
The Hubbard model, spin-and charge-density wave states, metal-insulator
transition. Review of harmonic theory of lattice vibrations. Anharmonic
effects. Electron-phonon interaction – phonons in
metals, mass renormalization, effective interaction between electrons, polarons. Transport phenomena, Boltzmann equation,
electrical and thermal conductivities, thermo-electric
effects. Superconductivity–phenomenology, Cooper instability,
BCS theory, Ginzburg-Landau theory.
Subroto MukerjeePH
Ashcroft,
N.W., and
Madelung, O., Introduction to
Jones,
W., and March, N.H., Theoretical
PH 322 (JAN) 3:0
Molecular
Simulation
Introduction to
molecular dynamics, various schemes for integration, inter- and intra-molecular
forces, introduction to various force fields, methods for partial atomic
charges, various ensembles (NVE, NVT, NPT, NPH), hard sphere simulations, water
imulations, computing long-range interactions.
Various schemes for minimization: conjugate radient,
steepest descents. Monte Carlo simulations, the Ising
model, various sampling methods, particle-based MC simulations, biased
Prabal K Maiti
Prerequisites: Basic
courses in statistical physics, quantum mechanics
Frenkel, D., and Smit, B., Understanding Molecular
Simulation, Academic Press, NY, 2001.
Allen, M.P., and Tildesley, D.J., Computer Simulation of Liquids,
PH 325 (AUG) 3:0
Advanced
Statistical Physics
Systems
and phenomena. Equilibrium and nonequilibrium models. Techniques for equilibrium
statistical mechanics, with examples, e.g., exact solution, mean field theory,
perturbation expansion, Ginzburg Landau theory, scaling, numerical methods. Critical
phenomena, classical and quantum. Disordered systems
including percolation and spin glasses. A brief survey
of non-equilibrium phenomena including transport, hydrodynamics, and
non-equilibrium steady states.
Rahul Pandit
Chaikin, P.M.,
and Lubensky, T.C., Principles of Condensed Matter
Physics,
Plischke, M., and Bergersen, B..
Equilibrium Statistical Physics, Second Edn,
World Scientific, 1994.
Sethna, J.P., Statistical Mechanics: Entropy, Order Parameters and
Complexity,
PH
330 (AUG) 0:3
Advanced
Independent Project In Physics
(open to research students only)
Faculty
PH 347 (AUG) 2:0
Bioinformatics
Biological databases: Organisation, searching and
retrieval of information, accessing global bioinformatics resources using the
World Wide Web. UNIX operating system and network
communication. Nucleic acid sequence assembly,
restriction mapping, finding simple sites and transcriptional signals, coding
region identification. Similarity and homology, dotmatrix methods, dynamic programming methods, scoring
systems, multiple sequence alignments, evolutionary relationships, genome
analysis. Protein structure classification, secondary
structure prediction, hydrophobicity patterns,
detection of motifs, structural databases (PDB), genome databases, structural
bioinformatics. Biological systems.
Topics from the current literature will be discussed.
Hands on experience will be provided.
Mount, D.W., Bioinformatics: Sequence and Genome
Analysis, Second Edn,
Zvelebil, M., and Baum, J.O.,
Understanding Bioinformatics,
Pevsner, J.,
Bioinformatics and Functional Genomics, Second Edition, Wiley-Blackwell,
2009.
PH
350
(JAN) 3:0
Physics
of Soft Condensed Matter
Phases of soft condensed matter;
colloidal fluids and crystals; polymer solutions, gels and melts; micelles,
vesicles, surfactant mesophases; polymer colloids, microgels and star polymers - particles with tunable soft repulsive interaction, surfactant and phospolipid membranes; lyotropic
liquid crystals. Structure and
Dynamics of soft matter; electrostatics in soft matter, dynamics at
equilibrium; glass formation and jamming, dynamical heterogeneity. Soft
glassy rheology; shear flow, linear and non-linear rheology; visco-elastic models;
Introductory Biological Physics; Active matter.
Experimental methods; Small angle scattering and
diffraction, Dynamic light scattering and diffusive wave spectroscopy; methods
for studying dynamics of soft matter using synchrotron x-ray and neutron
scattering; rheometry; confocal
microscopy.
Prerequisite: Knowledge of basic statistical mechanics
Jaydeep K Basu and Sriram Ramaswamy
Jones, R.A.L., Soft Condensed Matter,
Rubinstein, M., and Colby, R.H., Polymer physics,
Doi and Edwards, Theory of Polymer Dynamics, Clarendon,
Philip Nelson, Biological Physics: Energy, Information and Life, Freeman, 2003.
Phillips, R., Kondev, J., and Theriot, J.,
Physical Biology of the Cell,
Israelachvilli, J.N., Intermolecular and surface
forces, Second Edn, Academic press
W B Russel et al., Colloidal
Dispersions,
Safran, S.,
Statistical thermodynamics of surfaces, interfaces and membranes,
Gelbart,
Roux and Ben-Shaul, Micelles, Membranes, Micremulsions and Monolayers, Springer,
NY, 1994.
Chaikin, P.M., and Lubensky, T.C.,
Principles of condensed matter physics, Cambridge Univ. Press,
P-G de Gennes, Prost,
J., The physics of liquid crystals, Clarendon,
PH 351 (AUG) 2:0
Basic concepts:
nucleation phenomena, mechanisms of crystal growth, dislocations and crystal
growth, crystal dissolution, materials preparation and phase diagrams.
Experimental methods of crystal growth: growth from liquid-solid equilibria, growth from vapour-solid
equilibria, mono-component and multi-component
techniques. Special techniques: Thin film growth methods including LPE, MOCVD,
MBE, PLD, etc.
Suja Elizabeth
Laudise, R.A., Growth of Single
Brice, J.C.,
Hurle, D.T.J.,
(ed.), Handbook of
PH 352 (JAN) 3:0
Semiconductor
Physics and Technology
Semiconductor
fundamentals: band structure, electron and hole
statistics, intrinsic and extrinsic semiconductors, energy band diagrams, drift-diffusion
transport, generation- recombination, optical absorption and emission. Basic
semiconductor devices: on junctions, bipolar transistors, MOS capacitors,
field-effect devices, optical detectors and emitters. Semiconductor technology:
fundamentals of semi- conductor processing techniques; introduction to planar
technology for integrated circuits.
K
S R Koteshwara Rao
Seeger,
K., Semiconductor Physics, Springer-Verlag, 1990.
Sze, S.M., Physics of Semiconductor Devices, Wiley, 1980.
Muller,
K., and Kamins, T., Device Electronics for Integrated
Circuits, John Wiley and Sons, 1977.
Lee, H.H., Fundamentals
of Microelectronics Processing, McGraw Hill, 1985.
PH 359 (JAN) 3:0
Physics
at the Nanoscale
Introduction to
different nanosystems and their realization;
electronic properties of quantum confined systems: quantum wells, wires, nanotubes and dots. Optical properties of nanosystems: excitons and plasmons; photoluminescence, absorption spectra, vibrational and thermal properties of nanosystems;
zone folding. Raman characterization.
A
K Sood
Nanostructures: Theory
and Modelling, by C. Delerue
and M Lannoo, (Springer, 2006), by Saito, R., Dresselhaus, G., and Dresselhaus,
M.S., Physical Properties of Carbon Nanotubes,
HE 392/PH 392 (AUG) 3:0
Standard
Model of Particle Physics
Weak interactions before
gauge theory, V-A theory, two component neutrino, massive vector bosons.
Spontaneous symmetry breaking (U(1)/SU(2)), Higgs
mechanism and mass bounds, custodial symmetry, SU(2) X U(1) Lagrangian,
GIM mechanism, CP-violation, particle-antiparticle mixing: K/B systems, S,T,U
parameters and precision measurements. Topics in QCD: asymptotic freedom,
operator product expansion, deep inelastic scattering and Parton model.
N
D Hari Dass and B Ananthanarayan
Cheng, T.P., and Li,
L.F., Gauge Theory of Elementary Particle Physics,
Commins, E.D., and Bucksbaum, P.H., Weak
Interactions of Leptons and Quarks,
Quigg, C., Gauge
Theories of the Strong, Weak and Electromagnetic Interactions,
Benjamin-Cummings, 1983.
Georgi H., Weak
Interactions and Modern Particle Theory, Benjamin-Cummings, 1984. Donoghue, J.F., Golowich, E., and Holstein, B.R.,
Dynamics of the Standard Model,
Sterman, G., An Introduction to Quantum Field
Theory,
HE 395/PH 395 (AUG) 3:0
Quantum
Mechanics III
Relativistic
quantum mechanics, Klein-Gordon and Dirac equations. Antiparticles and hole theory. Nonrelativistic
reduction. Discrete symmetries P, C and T. Lorentz and
Poincare groups. Weyl and Majorana fermions. Scalar fields, Dirac fields. Canonical quantisation. Propagators. Interactions and Feynman diagrams. S-matrix.
Scattering cross sections, decay rates and non-relativistic
potentials. Loop diagrams and renormalisation.
Power counting and renormalisability.
Global and local symmetries. Noether theorem.
Sudhir Vempati
Bjorken, J.D.,
and Drell, S., Relativistic Quantum Mechanics,
McGraw-Hill, 1965.
Ryder, L.H., Quantum
Field Theory,
Sakurai, J.J., Advanced
Quantum Mechanics, Benjamin Cummings, 1967.
HE 396 / PH 396 (JAN) 3:0
Gauge
Field Theories
Path
integral formulation, generating functional. Grassmann path
integrals. Yukawa theory. Abelian gauge theories. QED processes and Ward identities. Loop diagrams and renormalisation. Lamb shift and anomalous magnetic moment. Nonabelian gauge theories. Spontaneous
symmetry breaking, Goldstone bosons. Faddeev-Popov ghosts. Callan-Symanzik
equation, beta function. Asymptotic freedom.
Sudhir Vempati
Cheng, T.P., and Li,
L.F., Gauge Theories of Elementary Particle Physics, Clarendon, 1984.
Pokorski, S.,
Gauge Field Theories,
Kaku, M., Quantum Field Theory: A Modern Introduction,
Weinberg, S., The Quantum Theory of Fields, Vol. II: Modern Applications,