MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
February 16, 2008
PROBLEM SET 2
REFERENCES: Peskin and Schro eder, Section 2.3 and part of 2.4, through p. 29. Also
Lecture Notes 1 (or Lec
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
March 2, 2008
LECTURE NOTES 2
NOTES ON THE EULER-MACLAURIN
SUMMATION FORMULA
These notes are intended to supplement the Casimir eect proble
253a/Schwartz
Due Nov 4, 2015
Problem Set 8
1. Moller scattering is the process ee ee. Of the tree-level processes in QED in is
especially interesting because it involves identical particles.
a) Calculate the spin-averaged differential cross section for M
Physics 218
Solution Set #3
Winter 2016
1. In class, I defined the matrix-valued covariant derivative operator in the adjoint representation, D , by
D V (D V )a T a = V + ig[A , V ] ,
(1)
where V V a T a is a matrix-valued adjoint field and (D )ab ab + gf
An
overview of
SU(5)
grand
unification
Nicola
Canzano
An overview of SU(5) grand unification
Nicola Canzano
Physics Dept. University of California, Santa Cruz
March 2016
A Quick Review of the Standard Model (1)
An
overview of
SU(5)
grand
unification
Nicol
Physics 218
Solution Set #2
Winter 2016
1. Consider a field theory of a real pseudoscalar field coupled to a fermion field. The interaction
Lagrangian is:
Lint = i (x) 5 (x)(x) ,
where is a real coupling constant (called the Yukawa coupling). Using functi
Physics 218
Problem Set #2
Winter 2016
DUE: THURSDAY, FEBRUARY 11, 2016
1. Consider a field theory of a real pseudoscalar field (x) coupled to the electron field (x).
The interaction Lagrangian is:
Lint = i (x) 5 (x)(x) ,
where is a real coupling constant
Physics 218
Solution Set #4
Winter 2016
1. Consider the spontaneous breaking of a gauge group G down to U(1). The unbroken
generator Q = ca T a is some real linear combination of the generators of G.
Before we solve parts (a)(d) of this problem, we review
Physics 218
Problem Set #4
Winter 2016
DUE: THURSDAY, MARCH 17, 2016
1. Consider the spontaneous breaking of a gauge group G down to U(1). The unbroken
generator Q = ca T a is some real linear combination of the generators of G.
(a) Prove that xb cb /gb i
Physics 218
Problem Set #1
Winter 2016
DUE: THURSDAY, JANUARY 21, 2016
1. Show that for complex scalar fields,
Z
Z
Z
4
4
4
D D exp i d x d y (x)M(x, y)(y) + i d x J (x)(x) + (x)J(x)
Z
1
4
4
1
=N
exp i d x d y J (x)M (x, y)J(y) ,
det M
for some infin
Physics 218
Problem Set #3
Winter 2016
DUE: TUESDAY, MARCH 1, 2016
1. In class, I defined the matrix-valued covariant derivative operator in the adjoint representation, D , by
D V (D V )a T a = V + ig[A , V ] ,
where V Va T a is a matrix-valued adjoint fi
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
April 7, 2008
PROBLEM SET 7
REFERENCES: Lecture Notes 6: Path Integrals, Greens Functions, and Gener
ating Functions, on the website. Peski
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
February 16, 2008
LECTURE NOTES 1
QUANTIZATION OF THE FREE SCALAR FIELD
As we have already seen, a free scalar eld can be described by the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
March 13, 2008
PROBLEM SET 5
REFERENCES: Lecture Notes #4: Dirac Delta Function as a Distribution, on
the website. Peskin and Schroeder, Se
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
May 7, 2008
PROBLEM SET 10
REFERENCES: Peskin and Schro eder, Sec. 3.6, Secs. 4.1-4.6, in addition to
lecture slides that will be posted.
P
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
April 2, 2008
LECTURE NOTES 6
PATH INTEGRALS, GREENS FUNCTIONS,
AND GENERATING FUNCTIONALS
In these notes we will extend the path integral
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
February 28, 2008
PROBLEM SET 3
REFERENCES: You may want to look at Quantum Field Theory: From Operators
to Path Integrals, by Kerson Huan
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
February 10, 2008
PROBLEM SET 1
Corrected Version
REFERENCES: Peskin and Schro eder, Sections 2.1 and 2.2.
Problem 1: The energy-momentum t
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
March 4, 2008
PROBLEM SET 4
REFERENCES: Lecture Notes #3: Distributions and the Fourier Transform, on
the website.
Problem 1: Evaluation of
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
March 23, 2008
PROBLEM SET 6
Corrected Version
REFERENCES: Lecture Notes #5: Path Integrals for One-particle Quantum Me
chanics, on the web
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
March 3, 2008
INFORMAL NOTES
DISTRIBUTIONS AND THE FOURIER TRANSFORM
Basic idea:
In QFT it is common to encounter integrals that are not we
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
March 13, 2008
INFORMAL NOTES
DIRAC DELTA FUNCTION AS A DISTRIBUTION
Why the Dirac Delta Function is not a Function:
The Dirac delta functi
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.323: Relativistic Quantum Field Theory I
Prof. Alan Guth
April 17, 2008
PROBLEM SET 8
DESCRIPTION: This problem set contains only the three problems held over
from the previous problem set. Howeve
Physics 218
Solution Set #1
Winter 2016
1. Show that for complex scalar fields and a positive definite hermitian operator M,
Z
Z
Z
4
4
4
D D exp i d x d y (x)M(x, y)(y) + i d x J (x)(x) + (x)J(x)
Z
1
4
4
1
exp i d x d y J (x)M (x, y)J(y) ,
=N
det M