# 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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### How does satisfying the Euler-Lagrange equation put a Classical Path on-shell?

I am thinking of what the Euler-Lagrange equation, $$\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{x}}\right) - \frac{\partial L}{\partial x} = 0$$ specifically represents in satisfying the ...
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### Path Integral Formulation [duplicate]

The contribution to the propagator from a particular trajectory is $e^{\frac{iS[x(t)]}{ћ}}$. Does anyone knows how to get to this $e^{\frac{iS[x(t)]}{ћ}}$? As in showing me any reliable source ...
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### Is the Symmetry factor different in Path integral Formalism?

Is the Symmetry factor different in Path integral Formalism and the Perturbation theory (canonical) formalism? For example, the order-1 4-point cross X diagram in the $\phi^4$ theory has symmetry ...
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### Principle of least action: $\frac{d S_{cl}}{dt_b} = \frac{\partial S_{cl}}{\partial t_b} + \frac{\partial S_{cl}}{\partial x_b}\dot{x}_b$

Question I cannot see how I can obtain the yellow highlighted section on the RHS from that of the LHS. The following equation can be found in both my lecture notes(*1) (page 9, equation 2.7) and is ...
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### Feynman Path Integral as a Quantization Scheme

Why isn't the path integral usually discussed as a quantization scheme, like geometric and deformation quantization? Was searching wikipedia for this.
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### Is the Path Integral formulation of QM just a mathematical tool? [closed]

Is the Path Integral formulation of QM just a mathematical tool or does it offer deep physical insights on the nature of QM? Is it just an alternate way to describe Quantum Mechanics? Could someone ...
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### Unsolved Potentials in Path Integral

I just started learning on path integral on my own. It seems that the path integral method is not always able to be solved, depending on the potential. On the other hand, these potentials are ...
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### Why are coherent states necessary for defining the fermionic path integral?

I am following the discussion of fermionic path integrals and Grassmann variables in QFT for the Gifted Amateur (ch. 28). It defines a coherent state for fermions $\rvert \eta \rangle$ as \begin{...
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### Derivation of Aharonov Bohm effect for Quasiparticles

I've noticed the following: Observation: Central results in the condensed matter physics rely on Aharonov Bohm-type arguments involving quasiparticles with fractional charge. However, I can't ...
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### Books on path integral methods [duplicate]

Are there advanced books on applications to physics of the method of path integral? I am aware of some of the standard textbooks on QFT, but looking for more advanced applications of the method.
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### Determinant of a propagator

Say I have a path integral $\int D \phi \exp(i S_0)$. $S_0$ is the usual free action $$S_0=\frac{1}{2}\int\phi (-\Box-m^2) \phi=\frac{1}{2}\int \phi G^{-1} \phi,$$ and at the moment I'm not ...
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### Lagrangian vs Hamiltonian and symmetry of a theory

It is said that since the path-integral formulation of quantum mechanics/or quantum field theory uses the Lagrangian rather than the Hamiltonian, as the fundamental quantity, it preserves all the ...
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### How to deal with boundary conditions for path integrals?

For non-relativistic quantum mechanics, the boundary conditions are rather simple to deal with, they are just \langle x_1, t_1 \vert x_2, t_2\rangle = \int_{x_1(t_1)}^{x_2(t_2)} \...
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### Why does Feynman say that Huygens' principle is not correct for optics?

I am reading Feynman's famous paper Space-Time Approach to Non-Relativistic Quantum Mechanics, and in section 7 he says: Actually, Huygens' principle is not correct in optics. It is replaced by ...
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### Equivariant cohomology formula

I'm studying equivariant cohomology on three references: Szabo's review about equivariant localization (S); Libine's note on equivariant cohomology (L); Berline, Getzler, Vigne's book "Heat Kernels ...
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### How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?

I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
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### recovering numerical wave function using path integral after Wick rotation

I have written two different path-integral codes, PATHINT and PATHTREE, to numerically solve some classical-physics problems in nonlinear systems, finance and neuroscience. They work just fine. My ...
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### Chern-Simons function

The Chern-Simons function on the space of connections, mod the gauge transformations, on a 3-manifold can be defined by an integral. I study mathematics as profession, so I want to know what is the ...
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### Regularization of the 1-dimensional Laplacian

Disclaimer: this is a technical question about regularization of functional determinants which comes from a person with (relatively) strong background in QFT, string theory and path integrals, who ...
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