QFT Flashcards
What is the free Lagrangian of a real scalar theory?
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What is the field operator for a free real scalar theory?
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What is the relation between the momentum operator and the field operator in general?
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What is the conjugate momentum operator for a real scalar theory?
partial_0 (phi)
What is the equal time commutator for a real scalar theory?
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What is the commutation relation between operators in a real scalar theory?
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What is the formula for changing the argument of a delta function?
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What is the general form of a Hamiltonian density?
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What is the FT form of a delta function?
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What is the causality operator for the field operator?
Commutator of the field operator with itself.
ā>check integral form
What is the free Lagrangian for a complex scalar theory?
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What are the forms of the field operators for a complex scalar theory?
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What are the particle-field duality relations for a complex scalar field theory?
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What is the form of the conserved current in a complex scalar theory?
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What is the general form of the conserved charge operator?
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What is the interaction form of an operator in terms of the schrodinger form?
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What is the hamiltonian form of an operator in terms of the schrodinger form?
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How can we show the form of the time evolution operator?
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.
*donāt forget to change H_S to H_I
What is the integral form of the time evolution operator?
How is the S-matrix operator related to this?
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What is the form of the dirac Lagrangian?
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What is the form of a fermion field operator?
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What are the properties of fermion spinors u and v?
-EOM
-normalisation
-conjugate
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What is the form of the conjugate momenta for a fermion field operator?
i (field operator hermitian conjugate)
What are the equal time (anti)commutation relations for fermion field operators?
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What are the equal time (anti)commutation relations for fermion theory operators?
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How can we derive the form of the fermion propagator?
Show that it is equal to
[i (slash partial) + m] acting on the Feynman scalar propagator
How can we modify a lagrangian to give local U(1) invariance?
i partial_mu ā> i partial_mu - e A_mu
What is the QED lagrangian? (no gauge fixing)
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What is the form of the photon field operator?
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What is the conjugate momenta to the photon field operator?
partial_t (fermion field operator)
What is the equal time commutator for photon fields?
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What is the equal time commutator for photon operators?
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What are the forms of LH (contravariant) and RH (covariant) Weyl spinors?
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What are Weyl spinors?
2D complex vectors with anticommutative components
What are the commutation relations between Weyl spinors?
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What does duality of Weyl spinors refer to?
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What is the metric of the Weyl spinor space?
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How do Weyl spinors Lorentz transform?
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What are the forms of the three pauli matrices?
1 - ones antidiagonal
2 - iās antidiagonal (top negative)
3 - ones diagonal (bottom negative)
How can we form a dirac spinor from Weyl spinors?
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What is the relation between a bar dirac spinor and a dirac spinor?
hermitian conjugate x gamma_0
What is the form of the gamma matrix?
pauli matrices anti-diagonal
bottom pauli matrice barred - negative 1,2,3 components
What is the multiplication of two pauli matrices i and j?
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What are the two clifford algebra?
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What is the form of the EM field tensor?
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What is required for a graph to be UV finite?
negative superficial degree of divergence
as well as for ALL subgraphs
What must we remember for closed fermion loops in feynman diagrams?
apply (-1) factor
take the trace
What is a key property of traces?
Cyclic
What factor do we use for graphs with multiple identical particles (either in intial state, final state, or inbetween)
factor 1/n!
What is the feynman rule for a lepton/lepton/photon interaction?
-ie gamma_mu
What is the feynman rule for a scalar field propagator?
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What is the feynman rule for a photon propagator?
(-i eta_mu_nu) / (k^2 + i E)
What is the feynman rule for a lepton propagator?
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What MUST we remember for graphs with leptons or photons?
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)
What is the schrodinger picture of operators?
Operators are not time dependent
What is the optical theorem?
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