QFT

Question 1

What is the free Lagrangian of a real scalar theory?

Answer 1

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Question 2

What is the field operator for a free real scalar theory?

Answer 2

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Question 3

What is the relation between the momentum operator and the field operator in general?

Answer 3

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Question 4

What is the conjugate momentum operator for a real scalar theory?

Answer 4

partial_0 (phi)

Question 5

What is the equal time commutator for a real scalar theory?

Answer 5

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Question 6

What is the commutation relation between operators in a real scalar theory?

Answer 6

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Question 7

What is the formula for changing the argument of a delta function?

Answer 7

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Question 8

What is the general form of a Hamiltonian density?

Answer 8

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Question 9

What is the FT form of a delta function?

Answer 9

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Question 10

What is the causality operator for the field operator?

Answer 10

Commutator of the field operator with itself.
–>check integral form

Question 11

What is the free Lagrangian for a complex scalar theory?

Answer 11

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Question 12

What are the forms of the field operators for a complex scalar theory?

Answer 12

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Question 13

What are the particle-field duality relations for a complex scalar field theory?

Answer 13

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Question 14

What is the form of the conserved current in a complex scalar theory?

Answer 14

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Question 15

What is the general form of the conserved charge operator?

Answer 15

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Question 16

What is the interaction form of an operator in terms of the schrodinger form?

Answer 16

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Question 17

What is the hamiltonian form of an operator in terms of the schrodinger form?

Answer 17

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Question 18

How can we show the form of the time evolution operator?

Answer 18

Matrix elements are independent
–>relate an I state to a H state

Diff. eqn. involving time evolution operator by considering i partial_t acting on an I state.
*don’t forget to change H_S to H_I

Question 19

What is the integral form of the time evolution operator?
How is the S-matrix operator related to this?

Answer 19

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Question 20

What is the form of the dirac Lagrangian?

Answer 20

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Question 21

What is the form of a fermion field operator?

Answer 21

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Question 22

What are the properties of fermion spinors u and v?
-EOM
-normalisation
-conjugate

Answer 22

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Question 23

What is the form of the conjugate momenta for a fermion field operator?

Answer 23

i (field operator hermitian conjugate)

Question 24

What are the equal time (anti)commutation relations for fermion field operators?

Answer 24

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Question 25

What are the equal time (anti)commutation relations for fermion theory operators?

Answer 25

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Question 26

How can we derive the form of the fermion propagator?

Answer 26

Show that it is equal to [i (slash partial) + m] acting on the Feynman scalar propagator

Question 27

How can we modify a lagrangian to give local U(1) invariance?

Answer 27

i partial_mu --> i partial_mu - e A_mu

Question 28

What is the QED lagrangian? (no gauge fixing)

Answer 28

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Question 29

What is the form of the photon field operator?

Answer 29

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Question 30

What is the conjugate momenta to the photon field operator?

Answer 30

partial_t (fermion field operator)

Question 31

What is the equal time commutator for photon fields?

Answer 31

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Question 32

What is the equal time commutator for photon operators?

Answer 32

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Question 33

What are the forms of LH (contravariant) and RH (covariant) Weyl spinors?

Answer 33

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Question 34

What are Weyl spinors?

Answer 34

2D complex vectors with anticommutative components

Question 35

What are the commutation relations between Weyl spinors?

Answer 35

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Question 36

What does duality of Weyl spinors refer to?

Answer 36

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Question 37

What is the metric of the Weyl spinor space?

Answer 37

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Question 38

How do Weyl spinors Lorentz transform?

Answer 38

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Question 39

What are the forms of the three pauli matrices?

Answer 39

1 - ones antidiagonal 2 - i's antidiagonal (top negative) 3 - ones diagonal (bottom negative)

Question 40

How can we form a dirac spinor from Weyl spinors?

Answer 40

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Question 41

What is the relation between a bar dirac spinor and a dirac spinor?

Answer 41

hermitian conjugate x gamma_0

Question 42

What is the form of the gamma matrix?

Answer 42

pauli matrices anti-diagonal bottom pauli matrice barred - negative 1,2,3 components

Question 43

What is the multiplication of two pauli matrices i and j?

Answer 43

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Question 44

What are the two clifford algebra?

Answer 44

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Question 45

What is the form of the EM field tensor?

Answer 45

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Question 46

What is required for a graph to be UV finite?

Answer 46

negative superficial degree of divergence as well as for ALL subgraphs

Question 47

What must we remember for closed fermion loops in feynman diagrams?

Answer 47

apply (-1) factor take the trace

Question 48

What is a key property of traces?

Answer 48

Cyclic

Question 49

What factor do we use for graphs with multiple identical particles (either in intial state, final state, or inbetween)

Answer 49

factor 1/n!

Question 50

What is the feynman rule for a lepton/lepton/photon interaction?

Answer 50

-ie gamma_mu

Question 51

What is the feynman rule for a scalar field propagator?

Answer 51

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Question 52

What is the feynman rule for a photon propagator?

Answer 52

(-i eta_mu_nu) / (k^2 + i E)

Question 53

What is the feynman rule for a lepton propagator?

Answer 53

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Question 54

What MUST we remember for graphs with leptons or photons?

Answer 54

Require a factor for initial/final state particles. INITIAL lepton - u anti-lepton - vbar photon - epsilon^mu (k and lambda dependence) FINAL lepton - ubar anti-lepton - v photon - epsilon*^mu (k and lambda dependence)

Question 55

What is the schrodinger picture of operators?

Answer 55

Operators are not time dependent

Question 56

What is the optical theorem?

Answer 56

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