# Questions tagged [path-integral]

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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### Why path integral approach may suffer from operator ordering problem?

In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path. What did ...
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### In what sense is the proper/effective action $\Gamma[\phi_c]$ a quantum-corrected classical action $S[\phi]$?

There is a difference between the classical field $\phi(x)$ (which appears in the classical action $S[\phi]$) and the quantity $\phi_c$ defined as $$\phi_c(x)\equiv\langle 0|\hat{\phi}(x)|0\rangle_J$$ ...
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### Why does the classical path give the dominant contribution in the path integral?

Why is it that the classical path gives the dominant contribution in the quantum mechanical path integral? How do we understand this?
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### Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
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### Proof that the effective/proper action is the generating functional of one-particle-irreducible (1PI) correlation functions

In all text book and lecture notes that I have found, they write down the general statement \frac{\delta^n\Gamma[\phi_{\rm cl}]}{\delta\phi_{\rm cl}(x_1)\ldots\delta\phi_{\rm cl}(x_n)}...
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### Quantum mechanics textbooks that use path integrals

I'm looking for a textbook in quantum mechanics that relies heavily on Green functions and the path integral formalism to supplement my QM books. I want to do some calculations using alternative ...
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### What is the constraint on the Gauge Potential in the Covariant Gauges?

One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term $$-\frac{(\partial_\mu A^{\mu})^2}{2\xi}$$ to the Lagrangian. ...
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### Semiclassical limit of Quantum Mechanics

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...
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### Path integral derivation of the state-operator correspondence in a CFT

Below, I paraphrase the path integral derivation of the state-operator correspondence in chapter 4 of David Tong's string theory notes (see pdf here). This is my interpretation of the text in that pdf,...
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### Physical meaning of partition function in QFT

When we have the generating functional $Z$ for a scalar field Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\left[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\right]}, \end{...
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### Ward identity derived from global symmetry and SDE, different from that derived from gauge symmetry?

In QED, according to Schwinger-Dyson equation $^{[1]}$, \left(\eta^{\mu\nu}(\partial ^2)-(1-\frac{1}{\xi})\partial^{\mu}\partial^{\nu}\right)\langle 0|\mathcal{T}A_{\nu}(x)...|0\rangle = e\,\langle ...
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Once a quantum partition function is in path integral form, does it contain any operators? I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where $H$ is an operator, the Hamiltonian of the ...