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EXAMS January 2023 > QFT > Flashcards

QFT Flashcards

1
Q

What is the free Lagrangian of a real scalar theory?

A

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2
Q

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

A

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3
Q

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

A

-

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4
Q

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

A

partial_0 (phi)

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5
Q

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

A

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6
Q

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

A

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7
Q

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

A

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8
Q

What is the general form of a Hamiltonian density?

A

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9
Q

What is the FT form of a delta function?

A

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10
Q

What is the causality operator for the field operator?

A

Commutator of the field operator with itself.
ā€“>check integral form

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11
Q

What is the free Lagrangian for a complex scalar theory?

A

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12
Q

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

A

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13
Q

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

A

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14
Q

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

A

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15
Q

What is the general form of the conserved charge operator?

A

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16
Q

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

A

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17
Q

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

A

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18
Q

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

A

Matrix elements are independent
ā€“>relate an I state to a H state

Diff. eqn. involving time evolution operator by considering i partial_t acting on an I state.
*donā€™t forget to change H_S to H_I

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19
Q

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

A

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20
Q

What is the form of the dirac Lagrangian?

A

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21
Q

What is the form of a fermion field operator?

A

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22
Q

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

A

-

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23
Q

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

A

i (field operator hermitian conjugate)

24
Q

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

A

-

25
Q

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

A

-

26
Q

How can we derive the form of the fermion propagator?

A

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

27
Q

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

A

i partial_mu ā€“> i partial_mu - e A_mu

28
Q

What is the QED lagrangian? (no gauge fixing)

A

-

29
Q

What is the form of the photon field operator?

A

-

30
Q

What is the conjugate momenta to the photon field operator?

A

partial_t (fermion field operator)

31
Q

What is the equal time commutator for photon fields?

A

-

32
Q

What is the equal time commutator for photon operators?

A

-

33
Q

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

A

-

34
Q

What are Weyl spinors?

A

2D complex vectors with anticommutative components

35
Q

What are the commutation relations between Weyl spinors?

A

-

36
Q

What does duality of Weyl spinors refer to?

A

-

37
Q

What is the metric of the Weyl spinor space?

A

-

38
Q

How do Weyl spinors Lorentz transform?

A

-

39
Q

What are the forms of the three pauli matrices?

A

1 - ones antidiagonal
2 - iā€™s antidiagonal (top negative)
3 - ones diagonal (bottom negative)

40
Q

How can we form a dirac spinor from Weyl spinors?

A

-

41
Q

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

A

hermitian conjugate x gamma_0

42
Q

What is the form of the gamma matrix?

A

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

43
Q

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

A

-

44
Q

What are the two clifford algebra?

A

-

45
Q

What is the form of the EM field tensor?

A

-

46
Q

What is required for a graph to be UV finite?

A

negative superficial degree of divergence
as well as for ALL subgraphs

47
Q

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

A

apply (-1) factor
take the trace

48
Q

What is a key property of traces?

A

Cyclic

49
Q

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

A

factor 1/n!

50
Q

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

A

-ie gamma_mu

51
Q

What is the feynman rule for a scalar field propagator?

A

-

52
Q

What is the feynman rule for a photon propagator?

A

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

53
Q

What is the feynman rule for a lepton propagator?

A

-

54
Q

What MUST we remember for graphs with leptons or photons?

A

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)

55
Q

What is the schrodinger picture of operators?

A

Operators are not time dependent

56
Q

What is the optical theorem?

A

-

EXAMS January 2023 (4 decks)

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