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Centre for High Energy Physics

Indian Institute of Science, Bengaluru-560012

Ph.D. Programme

CHEP started a Ph.D. programme from the academic year 1996-97. The minimum qualification for applying is an M.Sc. in Physics, Mathematics or Chemistry, or a B.E./B.Tech. degree.

The programme is oriented towards research in theoretical and experimental high energy physics as well as mathematical physics. General research areas include: quantum field theory, the standard model of particle physics and beyond, new particle searches, collider data analysis, detector physics and fabrication, QCD and lattice gauge theories, quantum gravity, string theory and black holes, non-commutative geometry, quantum computation, condensed matter systems in low dimensions. The research interests of individual faculty members can be found in their respective home pages under Personnel.

The advertisement, examination, interview procedure, etc. are part of the overall procedure followed by IISc. The interviews for the CHEP programme are conducted by a departmental committee.

After admission, basic knowledge of the incoming students in the following subjects is checked: Classical mechanics, Electromagnetic theory, Mathematical physics, Quantum mechanics, Thermodynamics and statistical physics. During the first year, students are expected to fill up gaps in their knowledge, if necessary by solving a set of problems on the subjects.

Course requirements: 

          First semester           |          Second semester
         ----------------          |         -----------------
Quantum Mechanics III        3:0   |  Advanced Mathematical          3:0
Quantum Field Theory I       3:0   |    Methods in Physics
Elective E1 (One)            3:0   |  Elective E2 (One or Two)       3:0/6:0
                            -----  |                                ---------
                               9   |                                   6/9
                            -----  |                                ---------
          Third semester           |
         ----------------          |
Elective E3 (One or None)    3:0/0 |
                            -----  |
                               3/0 |

The minimum course credit requirement for the IISc Ph.D. programme is 18. The total course credit requirement for CHEP is higher---the list above ranges from 18 to 21 credits (because of the extra electives).
Electives (some electives may not be offered every year):
E1: Nuclear and Particle Physics (3:0),
    Advanced Statistical Physics (3:0),
    Condensed Matter Physics II (3:0).

E2: Quantum Field Theory II (3:0),
    General Relativity (3:0),
    Quantum Statistical Field Theory (3:0),
    Quantum Computation (3:0),
    String Theory (3:0),
    Experimental High Energy Physics (3:0).

E3: The Standard Model of Particle Physics (3:0),
    String Theory II (3:0),
    QCD and Collider Physics (3:0).

All the electives may not be offered every year. The students have
to choose the electives in consultation with their supervisors.
The supervisor may ask the students to take more electives than
the list above, even after the Comprehensive Exam, as per his/her
needs and interests.

There is no provision for skipping courses, but a student may seek exemption from any course by passing a written test at the beginning of the term.

Some of the courses overlap with those of the Physics department. The CHEP specific courses are: Nuclear and Particle Physics, Quantum Mechanics III, Quantum Field Theory I and II, Advanced Mathematical Physics, General Relativity, Quantum Computation, String Theory and II, The Standard Model of Particle Physics, Experimental High Energy Physics, and Collider Physics. The syllabi for these courses appear below.

There will be a Comprehensive Exam, which the students must take as soon as possible after passing the above courses. In any case, they must take the exam before the end of their second year. The exam will test whether the student has sufficient preparation to begin Ph.D. research. Those who fail the exam will be given another attempt after a few months.

At the time of joining, each student must find a provisional Faculty Advisor, who may not turn out to be the actual Ph.D. supervisor. The student must select the Ph.D. supervisor by the end of the second semester. Students will be permitted to work with a faculty outside CHEP if their research interests so demand. In such cases, however, they must have a joint supervisor in CHEP.

Beginning from the second year, students must present a seminar each year on their work, to acquaint the CHEP faculty with their progress.

Syllabi for the CHEP specific courses:

(a) HE 215 3:0 (AUG): 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. Hadron multiplets, composition of
mesons and baryons. Quark model and quantum chromodynamics.

Povh B., Rith K., Scholz C. and Zetsche F., Particles and Nuclei:
An Introduction to Physical Concepts (Second edition), Springer, 1999.
Krane K.S., Introductory Nuclear Physics,
John Wiley & Sons, 1988.
Griffiths D., Introduction to Elementary Particles
John Wiley & Sons, 1987.
Perkins D.H., Introduction to High Energy Physics (Third edition),
Addison-Wesley, 1987.

(b) HE 316 3:0 (JAN): Advanced Mathematical Methods in Physics ---

Symmetries and group theory. Finite and continuous groups with examples.
Group operations and representations. Homomorphism, isomorphism and
automorphism. Reducibility, equivalence, Schur's lemma. Permutation groups,
Young diagrams. Lie groups and Lie algebras. SU(2), SU(3) and applications.
Roots and weights. Dynkin diagrams. Classification of compact simple Lie
algebras. Exceptional groups. Elements of topology and homotopy.

Georgi H., Lie Algebras in Particle Physics (Second edition),
Perseus Books, 1999.
Mukhi S. and Mukunda N., Introduction to Topology, Differential Geometry
and Group Theory for Physicists, Wiley Eastern, 1990.
Hamermesh M., Group Theory and its Applications to Physical Problems,
Addison-Wesley, 1962.

(c) HE 384 3:0 (AUG): Quantum Computation ---

Foundations of quantum theory. States, observables, measurement and
unitary evolution. Qubits versus classical bits, spin-half systems
and photon polarisations. Pure and mixed states, density matrices.
Extension to positive operator valued measures and superoperators.
Decoherence and master equations. Quantum entanglement and Bell's theorems.
Introduction to classical information theory and generalisation to quantum
information. Dense coding, teleportation and quantum cryptography.
Turing machines and computational complexity. Reversible computation.
Universal quantum logic gates and circuits. Quantum algorithms: database
search, FFT and prime factorisation. Quantum error correction and fault
tolerant computation. Physical implementations of quantum computers.

Nielsen M.A. and Chuang I.L., Quantum Computation and Quantum Information,
Cambridge University Press, 2000.
Preskill J., Lecture Notes for the Course on Quantum Computation,
Peres A., Quantum Theory: Concepts and Methods,
Kluwer Academic, 1993.

(d) HE 386 3:0 (JAN): Experimental High Energy Physics ---

Particles and interactions in the standard model. Strong, weak and
electromagnetic interactions. Kinematics of particle interactions.
Concepts of accelerators, linear and circular Accelerators. Introduction
to particle detectors, interaction of particles with matter. Gaseous
detectors, scintillator detectors, solid state detector. Readout
electronics, vertex detection and tracking. Calorimetry for electrons,
photons, charged hadrons and neutrons. Particle identification and
detector systems. Experimental tests of the building blocks of matter
and their fundamental interactions. Examples of QCD tests, top quark,
Z and W bosons, Higgs boson, new particle searches. Review of some
particle physics experiments, concepts of collider physics, basic
phenomenology of a hard scattering process. Data analysis techniques
in collider physics, statistical analysis in particle physics.

Perkins D.H., Introduction to High Energy Physics (Third edition),
Addison-Wesley, 1987.
Leo W.R., Techniques for Nuclear and Particle Physics Experiments:
A How to Approach (Second revised edition)
Narosa/Springer International, 2012.
Knoll G.F., Radiation Detection and Measurement (Fourth edition),
Wiley, 2010.
Grupen C. and Schwartz B., Particle Detectors (Second edition),
Cambridge University Press, 2011.
Fernow R.C., Introduction to Experimental Particle Physics
Cambridge University Press, 1986.

(e) HE 388 3:0 (JAN): QCD and Collider Physics
    (Prerequisites: Quantum Field Theory I and
    The Standard Model of Particle Physics)

Review of perturbative QCD. Monte Carlo simulations and event generators.
Jet physics, event shape variables. Tests of the structure of QCD, jet
substructure analysis. Introduction to lepton and hadron collider basics.
Higgs and heavy quark production at the LHC, search for new physics at the
LHC. Supersymmetry, extra dimensions and dark matter. Statistical analysis
and limit setting.

Ellis R., Stirling W. and Webber B., QCD and Collider Physics,
(Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology)
Cambridge University Press, 1996.
Plehn T., Lectures on LHC Physics,
Springer, 2012 [arXiv:0910.4182v6].
Barger V.D. and Phillips R.J.N., Collider Physics (updated edition),
CRC Press, 1996.
Cowan G., Statistical Data Analysis 
Oxford Science Publications, 1998.

(f) HE 391 3:0 (AUG): Quantum Mechanics III ---

Path integrals in quantum mechanics. Action and evolution kernels.
Free particle and harmonic oscillator solutions. Perturbation theory,
transition elements. Fermions and Grassmann integrals. Euclidean
time formulation, statistical mechanics at finite temperature.
Relativistic quantum mechanics, Klein-Gordon and Dirac equations.
Antiparticles and hole theory. Klein paradox. Nonrelativistic reduction.
Coulomb problem solution. Symmetries P, C and T, spin-statistics theorem.
Lorentz and Poincare groups. Wigner classification of single particle
states. Weyl and Majorana fermions. Modern topics such as graphene,
Kubo formulae. Introduction to conformal symmetry and supersymmetry.

Feynman R.P. and Hibbs A.R., Quantum Mechanics and Path Integrals,
McGraw-Hill, 1965.
Bjorken J.D. and Drell S., Relativistic Quantum Mechanics,
McGraw-Hill, 1965.
Greiner W., Relativistic Quantum Mechanics: Wave Equations (Third edition),
Springer, 1990.
Peskin M.E. and Schroeder D.V., An Introduction to Quantum Field Theory,
Addison Wesley,	1995.

(g) HE 392 3:0 (JAN): String Theory ---
    (Prerequisite: Quantum Field Theory I)

Bosonic Strings: closed and open, oriented and unoriented. Light cone
quantization and spectrum. Polyakov path integral. BRST symmetry.
Conformal field theory. Modular invariance. Boundary states.
Classical and quantum superstrings. Spin structures and GSO projection.
Type II strings. D-branes and Type I strings. Torus compactification
and Heterotic strings. Current algebras and lattices. Bosonization.
N=1,2 superconformal field theory.

Green M.B., Schwarz J.H. and Witten E., Superstring Theory, Vol. I and II,
Cambridge University Press, 1989.
Polchinski J., String Theory, Vol I and II,
Cambridge University Press, 2005.
Kiritsis E., String Theory in a Nutshell,
Princeton University Press, 2007.

(h) HE 393 3:0 (AUG): String Theory II ---
    (Prerequisite: String Theory)

Continuation of torus reductions and heterotic strings. D-branes again,
this time via T-duality. Superconformal field theories. Picture changing.
Spacetime supersymmetry. Effective supergravity. D-brane actions.
Orbifolds and orientifolds. Calabi-Yau compactification and connections
to phenomenology. Green-Schwarz mechanism. BPS states and p-branes.
Web of string dualities. M-theory and F-theory. Black Holes and
AdS/CFT correspondence.

Green M.B., Schwarz J.H. and Witten E., Superstring Theory, Vol. I and II,
Cambridge University Press, 1989.
Polchinski J., String Theory, Vol I and II,
Cambridge University Press, 2005.
Kiritsis E., String Theory in a Nutshell,
Princeton University Press, 2007.
Blumhagen R., Lust D. and Theisen S., Basic Concepts of String Theory,
Springer, 2013.

(i) HE 395 3:0 (AUG): Quantum Field Theory I ---

Scalar, spinor and vector fields. Canonical quantisation, propagators.
Symmetries and Noether theorem. Path integrals for bosonic and
fermionic fields, generating functionals. Feynman diagrams.
S-matrix, LSZ reduction formula. Interacting scalar and Yukawa theories.
Covariant derivatives and gauge theories. Quantum electrodynamics.
Gauge invariance, massless photons, Ward identity. Elementary processes.
Scattering cross-sections, optical theorem, decay rates. Loop diagrams,
power counting, divergences. Renormalization, fixed point classification.
One loop calculations in QED. Callan-Symanzik equations, beta functions.
Effective field theory.

Zee A., Quantum Field Theory in a Nutshell (Second edition),
Princeton University Press, 2010.
Srednicki M., Quantum Field Theory,
Cambridge University Press, 2007.
Ryder L.H., Quantum Field Theory (Second edition),
Cambridge University Press, 1996.
Ramond P., Field Theory: A Modern Primer (Second edition),
Levant Books, 2007.

(j) HE 396 3:0 (JAN): Quantum Field Theory II ---
    (Prerequisite: Quantum Field Theory I)

Abelian gauge theories. QED processes and symmetries. Loop diagrams
and 1-loop renormalization. Lamb shift and anomalous magnetic moments.
Nonabelian gauge theories. Faddeev-Popov ghosts. BRST quantization.
QCD beta function, asymptotic freedom. Spinor helicity formalism for
gauge theories. Composite operators, operator product expansion.
Anomalies. Lattice gauge theory, strong coupling expansion.
Confinement and chiral symmetry breaking.

Schwartz M.D., Quantum field theory and the standard model,
Cambridge University Press, 2014.
Srednicki M., Quantum Field Theory,
Cambridge University Press, 2007.
Peskin M.E. and Schroeder D.V., An Introduction to Quantum Field Theory,
Addison Wesley,	1995.
Weinberg S., The Quantum Theory of Fields, Vol. I: Foundations,
Vol. II: Modern Applications, Cambridge University Press, 1996.

(k) HE 397 3:0 (AUG): The Standard Model of Particle Physics ---
    (Prerequisites: Quantum Field Theory I and II)

Weak interactions before gauge theory. V-A theory, massive vector bosons. 
Spontaneous symmetry breaking, Goldstone bosons, Higgs mechanism.
Charged and neutral currents, gauge symmetries and SU(2)xU(1) Lagrangian.
Flavour mixing, GIM mechanism. CP violation, K/B systems. Neutrinos.
Electroweak precision measurements. Deep inelastic scattering,
parton model. Chiral Lagrangians and heavy quark effective field theories.

Georgi H., Weak Interactions and Modern Particle Theory,
Benjamin/Cummings, 1984.
Halzen F. and Martin A.D., Quarks and Leptons: An Introductory Course
in Modern Particle Physics, John Wiley & Sons, 1984.
Pokorski S., Gauge Field Theories (Second edition),
Cambridge University Press, 2000.
Peskin M.E. and Schroeder D.V., An Introduction to Quantum Field Theory,
Addison Wesley,	1995.

(l) HE 398 3:0 (JAN): General Relativity

Review of tensor calculus and properties of the Riemann tensor.
Killing vectors, symmetric spaces. Geodesics. Equivalence principle
and its applications. Scalars, fermions and gauge fields in curved
space-time. Einstein's equations and black hole solutions.
Schwarzschild solution, Motion of a particle in the Schwarzschild
metric. Kruskal extension and Penrose diagrams. Reissner-Nordstrom
solution, Kerr solution. Laws of black hole physics. Gravitational
collapse. Oppenheimer-Volkoff and Oppenheimer-Snyder solutions,
Chandrasekhar limit. Cosmological models, Friedmann-Robertson-Walker
metric. Open, closed and flat universes. Introduction to quantizing
fields in curved spaces and Hawking radiation.

Landau L.D. and Lifshitz E.M., The Classical Theory of Fields,
Pergamon Press, 1975.
Weinberg S., Gravitation and Cosmology:
Principles and Applications of the General Theory of Relativity,
John Wiley & Sons, 1972.
Wald R.M., General Relativity,
Overseas Press, 2006.
't Hooft G., Inroduction to General Relativity,
Introduction to the theory of Black Holes,

(m) HE 379: Physics Beyond Standard Model

Higgs discovery and its implications, effective field theories, 
supersymmetry and supergravity, extra dimensions and its variants,  
composite Higgs models,  Cosmological solutions like relaxions and 
its variants, neutrino masses and GUTS,  axions, and  modern probes 
of new physics. 
Prerequisites:  All QFT courses , Standard Model and  preferably GTR.



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