# Tagged Questions

Path integral formulation (Due to Feynman) is a major formulation of Quantum Mechanics along with Matrix mechanics (Due to Heisenberg and Pauli), Wave Mechanics (Due to Schrodinger), and Variational Mechanics (Due to Dirac). DO NOT USE THIS TAG for line/contour integrals.

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### Is it possible to do a path integral between two boundaries analytically on a quantum lattice?

I have been trying to perform some path integral between two boundaries for a massless scalar field $$\int_{\varphi(t_a, \vec{x})}^{\varphi(t_b, \vec{x})} \mathcal{D}\varphi(x)e^{iS[\varphi(x)]}$$ ...
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### When can the source term of a partition function be put in?

More specifically, in quantum field theory books, we usually have this: Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + \bar{\psi}...
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### ${\phi}^4$ description of Ising ferromagnet

Suppose the coupling between two spins is $C_{i,j}<0$, then the classical partition function is given by $$Z=\sum_{\{s_i\}}e^{\sum_{i,j}s_iK_{ij}s_j+h\sum_{i}s_i}$$ where $K_{ij}=-\beta C_{ij}$ and ...
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### Fermionic path integral on the disk - Recovering the vacuum state

I'm trying to get a better feel for the operator to state map in quantum field theory. There is a general claim for 2d theories that doing the path integral on a disk with no operator insertions gives ...
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### Polology in Functional Integration

Completeness of Hilbert space (on-shell states) is a very powerful concept in canonical quantization, for example, to study the nonperturbative characteristics of the S-matrix, like polology (pole and ...
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### Weinberg's spontaneous broken symmetries

Steven Weinberg in his second volume of QFT's book (in section about spontaneously broken symmetries, in subsection about Goldstone bosons) writes following: if we have linear transformation of ...
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### When can I use semiclassical approximation?

I know that I can use semiclassical approximation for path integral approach (in quantum mechanics) $\int d[q]e^{iA}$ when action $A >>1$. But how shall I use such condition? For example, ...
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### How to arrive on the diffraction pattern for the double slit experiment using path integrals for the Gaussian slit case?

I wish to take the path integral route to derive the diffraction pattern for the double slit experiment using the Gaussian slits as the nature of the slits. The kernel looks like: K((...
I keep seeing this for the vacuum to vacuum transition amplitude: $\langle 0,\infty|0,-\infty\rangle_J\,.$ What is $|0,-\infty\rangle_J?$ Am I to take the Hamiltonian with the source present, ie. $H(t)... 0answers 268 views ### Epstein-Glaser causal perturbation theory Why does causal perturbation theory in the sense of Epstein Glaser fall under algebraic QFT rather than heuristic QFT in renormalization? 0answers 91 views ### If you are only interested in deriving Feynman diagrams can you skip path integrals and just compute greens functions? I've been reading about the path integral approach to quantum field theory and I noticed that at the end you are just computing greens functions that you could have started computing in the beginning. ... 0answers 158 views ### Deriving effective model without integrating out degrees of freedom in path integral formalism? In path integral formalism of quantum field theory (particle physics or condensed matter), one can in principle integrate out part of the degrees of freedom so as to attain an effective model ... 0answers 67 views ### Anomaly and Weyl spinors I try to better understand anomalies in QFT and I've got a question concerning derivation of axial anomaly in Terning's lectures (page 12) Consider a theory of Weyl fermions coupled to a gauge field$...
Consider the field being decomposed into a orthogonal and completed basis: $\Phi(x) = \sum_n c_n \phi_n(x)$ (or $\Phi(x) = \int dk c_k \phi_k (x)$, if continuous) The notation: \$\phi_n(x) = <x|\...