U NIVERSITY OF C AMBRIDGE
PART III M ATHEMATICS
Quantum Field Theory
M ICHAELMAS TERM 2013
Based on Lectures by:
Prof. Malcolm Perry
Last updated: 17th May 2014
Typeset by:
Alice Harpole
Preface
I typeset these notes over the winter vacation for the Micha
Consumers and Business Ethics
Prepared for class discussion
By
Prof.S.Suryanarayanan
Consumers as stakeholders (I)
Commonplace argument that businesses are best served by treating their
customers well
So why continued ethical abuses of consumers and poo
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (Energy transfer)
1- A gas in a pistoncylinder assembly undergoes an expansion process for which the
relationship between pressure and volume is given by pVn = constant
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
Revision (Pure Substances)
A rigid tank contains 50 kg of saturated liquid water at 90C. Determine the pressure in the
1- tank and the volume of the tank.
A pistoncylinder device cont
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (properties)
1-What a can of soft drink at room temperature is put into the refrigerator so that it will
cool. Would you model the can of soft drink as a closed system o
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (properties)
1-What a can of soft drink at room temperature is put into the refrigerator so
that it will cool. Would you model the can of soft drink as a closed system
o
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
ENGR 360 BLDG
Pre-Junior Students
Sheet (Combustion)
1- State the combustion equation, the corresponding mass balance and find the
A/F ratio for CH4 with air in chemically correct or
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (Energy transfer)
1- A gas in a pistoncylinder assembly undergoes an expansion process for which the relationship
between pressure and volume is given by pv n = constant
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (Ideal Gas)
1- Determine the mass of the air in a room whose dimensions are 4 m X 5 m X6 m at 100
kPa and 25C.
2- A pistoncylinder assembly contains 2 lb of air at a tem
Faculty of Engineering
Credit Hours Engineering Programs
Thermodynamics
MPE 112
Sheet (1st law)
1- system comprising of gas in cylinder at pressure of 689 kPa Fluid expands from a
volume of 0.04 m3 to 0.045 m3 while pressure remains constant. Paddle wheel
MATHEMATICAL TRIPOS
Part III
Friday, 3 June, 2011 9:00 am to 12:00 pm
PAPER 46
ADVANCED QUANTUM
FIELD THEORY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIRE
0. Introduction
There are no real one-particle systems in nature, not even few-particle
systems. The existence of virtual pairs and of pair uctuations shows that
the days of xed particle numbers are over.
Viki Weisskopf
The concept of wave-particle dualit
1.2 Lorentz Invariance
The laws of Nature are relativistic, and one of the main motivations to develop quantum
eld theory is to reconcile quantum mechanics with special relativity. To this end, we
want to construct eld theories in which space and time are
2. Free Fields
The career of a young theoretical physicist consists of treating the harmonic
oscillator in ever-increasing levels of abstraction.
Sidney Coleman
2.1 Canonical Quantization
In quantum mechanics, canonical quantization is a recipe that takes
Since the classical eld is not real, the corresponding quantum eld is not hermitian.
This is the reason that we have dierent operators b and c appearing in the positive
and negative frequency parts. The classical eld momentum is = L/ = . We
also turn this
Quantum Field Theory: Example Sheet 4
Prof N.S. Manton, Michaelmas Term 2010
1. A real scalar eld with 4 interaction has the Lagrangian density
Copyright 2010 University of Cambridge. Not to be quoted or reproduced without permission.
1
1
L = m2 2 4 .
2
2
Quantum Field Theory: Example Sheet 3
Prof N.S. Manton, Michaelmas Term 2010
1. The Weyl representation of the Cliord algebra is
Copyright 2010 University of Cambridge. Not to be quoted or reproduced without permission.
0 =
0 12
12 0
i =
,
0 i
i 0
(1)
.
Quantum Field Theory: Example Sheet 2
Prof. N.S. Manton, October 2010
1. A string has classical Hamiltonian given by
12
p
2n
H=
122
+ 2 n qn
(1)
Copyright 2010 University of Cambridge. Not to be quoted or reproduced without permission.
n=1
where n is the
Quantum Field Theory: Example Sheet 1
Prof. N.S. Manton, October 2010
Copyright 2010 University of Cambridge. Not to be quoted or reproduced without permission.
1. A string of length a, mass per unit length and under tension T is xed at each
end. The Lagr
Mathematical Tripos Part III
Advanced Quantum Field Theory: Examples 4
Lent Term 2011
N. Dorey
Gauge Theories
1. Let cfw_T a with a = 1, . . . , N 2 1 be a set of generators in the fundamental representation of Lie (SU (N ).
The adjoint representation of
Mathematical Tripos Part III
Advanced Quantum Field Theory: Examples 3
Lent Term 2011
N. Dorey
Feynman Graph and RG Calculations
1. Consider a theory in 4 dimensions which contains both scalar elds and spinor elds . The interaction
lagrangian contains ver
Mathematical Tripos Part III
Advanced Quantum Field Theory: Examples 2
Lent Term 2011
N. Dorey
Functional Methods and Grassmann Integrals
1. Let, with x, b Rn ,
eW (b) =
dn x eS +bx ,
S=
1
2
x A x + V (x) .
Copyright 2011 University of Cambridge. Not to b
Mathematical Tripos Part III
Advanced Quantum Field Theory: Examples 1
Lent Term 2011
N. Dorey
Path Integrals and Feynman Graphs
Set
= 1 throughout.
Copyright 2011 University of Cambridge. Not to be quoted or reproduced without permission.
1. Let
1
2
(q q
MATHEMATICAL TRIPOS
Part III
Thursday, 2 June, 2011 9:00 am to 12:00 pm
PAPER 42
QUANTUM FIELD THEORY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
SPECIAL REQUIREMENTS
C
MATHEMATICAL TRIPOS
Thursday, 27 May, 2010
Part III
9:00 am to 12:00 pm
PAPER 42
QUANTUM FIELD THEORY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury T
MATHEMATICAL TRIPOS
Thursday, 28 May, 2009
Part III
9:00 am to 12:00 pm
PAPER 44
QUANTUM FIELD THEORY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury T
MATHEMATICAL TRIPOS
Thursday 29 May 2008
Part III
9.00 to 12.00
PAPER 48
QUANTUM FIELD THEORY
Attempt no more than THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Scrip
MATHEMATICAL TRIPOS
Friday 1 June 2007
Part III
9.00 to 12.00
PAPER 50
QUANTUM FIELD THEORY
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Script paper
SPECIAL
MATHEMATICAL TRIPOS
Thursday 1 June, 2006
Part III
9 to 12
PAPER 48
QUANTUM FIELD THEORY
Attempt THREE questions.
There are FOUR questions in total.
The questions carry equal weight.
STATIONERY REQUIREMENTS
Cover sheet
Treasury Tag
Script paper
SPECIAL RE