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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Euler-Lagrange Equation in Quantum Field Theory

The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a ...
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Vacuum persistance amplitude

E. Fradkin's Field Theories in Condensed Matter Physics formulas 3.57 and 3.58: I feel really sad about it, but all my tries of getting from formula $$ Z = \operatorname{tr} \hat{T} \prod_{j=1}^{...
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143 views

Feynman's derivation of the Schrödinger equation

I'm reading the following article: Feynman's derivation of the Schrödinger equation In this article, the autor claims that Feynman derivation of the Schrödinger equation was a key aspect of the ...
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Wilsonian Renormalisation — Peskin & Schroder Sect. 12.1

I'm working my way through Peskin & Schroeder, but some of the details of the calculations done in their introduction to the renormalisation group are slipping past me. For concreteness, the ...
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Electron - neutrino scattering effective Lagrangian

The electron and neutrino can interact through an intermediary Z boson, via the Lagrangian: $$ L= \frac{1}{2} \partial_\mu \phi_Z \partial^\mu \phi_Z - \frac{1}{2} m_Z ^2 \phi_Z ^2 -g_{\nu} \phi_Z \...
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Partition function and coherent state path integral

I have been working through the derivation of the partition function expressed as a path integral in terms of coherent states, following the many-body condensed-matter field theory books of Altland &...
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78 views

Feynman propagator for photons and the actual propagation of photons

Reading some books of quantum field theory (c.f. LH Ryder. 'Quantum Field Theory') it seems that the concept of path integrals in quantum mechanics may be extended to the field theory using the ...
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85 views

Lack of Maslov index in the path integral formalism

Introduction Consider Feynman's famous path integral formula \begin{equation} K(x_a,x_b) = \int \mathcal{D}[x(t)] \exp \left[ \frac{i}{\hbar} \int_{t_a}^{t_b} dt \, \mathcal{L}(x(t),\dot{x}(t),t) \...
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Stratonovich integral in quantum field theory

I'm reading a paper on Wick renormalization and there are a couple of things that are not that clear to me. The paper ends with the following sentence: In Euclidean quantum field theory, the ...
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56 views

Quantum mechanics: Path integrals vs normal

What are the similarities and differences in the theory for quantum mechanics using path integrals versus the normal method using wave functions?
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Exchanging a local operator with a path integral

I am reading a paper by J. Polchinski, called "What is string theory", hep-th/9411028. In eq. 1.1.9, and the line before it, the author seems to have used: $$\langle \partial_z \partial_{\bar{z}} X(z,...
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Propagator from Path integral

In class we have proved something like: $$ \frac{\partial^2 Z(J,\bar{J})}{\partial J(x) \partial \bar{J}(x')}\frac{1}{Z}|_{J=\bar{J}=0}=\Delta(x-x').$$ That by introducing source terms to path ...
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Analyzing the free-particle kernel [closed]

I recently began studying the theory of path integrals from the book by Feynman and Hibbs. The Problem $3.6$ asks to give an argument to show that $F(t_b,t_a)$ depends only on $t_b-t_a$. ...
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56 views

Determinants in path integrals in gauge theories and geometry

I know that in the formalism of path integral it is easy to show how determinants, corresponding to gauge fixing condition and FP ghosts, appear. But there is strict explanation of these determinants ...
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Feynman's Path Integral Approach: The Complex Exponentiated Action [duplicate]

I'm working on a project covering Feynman's Path Integral Approach. I'm having trouble intuitively grasping what motivates the introduction of the expression $e^\frac{iS}{\hbar}$, where S is the ...
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61 views

Where is the BRST symmetry?

When quantizing YM we start from the gauge fixed path integral (to remove redundancy of integrating over Gauge symmetric configurations) $$\int \mathcal{D}A \delta(G(A)) \text{det} \Delta_{FP}e^{i\int ...
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In path integral of multiply connected manifold, how to prove the partial amplitudes are linear independent? [closed]

In path integral of multiply connected manifold $X$, $$K(b,t_b;a,t_a)=\sum_{\alpha\in \pi_{1}}\chi(\alpha)K^{\alpha}(b,t_b;a,t_a)$$ where $K^\alpha$ is called partial amplitude, $\alpha$ denotes the ...
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What's the Propagator in the Free Particle Case? (Path Integrals with Source Term)

If I take the Lagrangian to be, $$L(t)=\frac{1}{2}m \dot q(t)^2$$ The Euclidean Path Integral is supposed to be, $$K=\int D[q(t)] \ e^{-\int L(\dot q) d \tau}$$ If I add a source term $J(\tau)$ we ...
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Path integral (sum over paths where $v>c$) [closed]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
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139 views

Are the path integral formalism and the operator formalism inequivalent?

Abstract The definition of the propagator $\Delta(x)$ in the path integral formalism (PI) is different from the definition in the operator formalism (OF). In general the definitions agree, but it is ...
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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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Linear Response And path integral

I'm following Wen's book on Quantum field theory, and I'm struggling with section 2.2.1 on linear response and response functions. Specifically I'm unable to reproduce equation 2.2.7 in which the ...
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337 views

Physical meaning of partition function in QFT

When we have the generating functional $Z$ for a scalar field \begin{equation} Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\Big[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\Big]}, \end{...
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Estimation of an Entropic Path Integral

I'm trying to reproduce some results from a paper (http://www.alexwg.org/publications/PhysRevLett_110-168702.pdf for reference) and basically I need a way of estimating a particular path integral (...
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Itô or Stratonovich calculus: which one is more relevant from the point of view of physics?

Langevin equation provides an example of a physical model which involves a differential equation with a stochastic term. Now, I wonder, how should one treat this? When I studied stochastic processes, ...
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Path Integral Quantization in General Relativity

In Ref. 1 I have seen that the action must contain only the first derivative of the metric as required by the path integral approach. I don't understand why. I mean why the path integral approach of ...
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The central limit theorem from a path integral?

On https://en.wikipedia.org/wiki/Path_integral_formulation it is noted that the central limit theorem can be interpreted as the first historical evaluation of a statistical path integral. Is this true?...
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Addtional QFT Book synergetic to Srednicki. Differences $\phi^4$ and $\phi^3$ [duplicate]

I currently hear a course to basic QFT in path integral formulation. Focus is on few and elementary particles, not on many body systems. The lecturer follows the book of Srednicki, which therefore ...
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Feynman path integral course online [duplicate]

There are a lot of books dealing with Feynman path integrals. Are there any online courses introducing Feynman path integrals and their applications?
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112 views

Are path integrals integrals with countable or uncountable infinite dimensions?

Path integrals are integrals with infinite dimensions. But I recently became confused about if the number of dimensions are discrete/countable or continuous/uncountable. I always thought it should be ...
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54 views

How to get anti-commuting rule from the view of field?

I was reading the 1951 Lectures on Advanced Quantum Mechanics and I found something really disturbing. That's the anti-commuting rule mentioned on Page 40 at last. Though it was named as Quantum ...
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98 views

Geometric derivation of quantum mechanics from Lagrangian mechanics

I have used classical Lagrangian mechanics for quite a while, and what I like about it is that everything can be derived from a very small number of geometric principles. There are just three things ...
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General properties of Matsubara frequency summations

By properties such as linearity, shifting, commutativity, etc. I was hoping to evaluate something like, $$S_\eta = \dfrac{1}{\beta}\displaystyle\sum_{i\omega} \dfrac{i\omega-\xi_1}{[(i\omega-\xi_2)^2-...
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Motivation for integrals over scalar field

I'm looking for good examples of physical motivation for integrals over scalar field. Here is an example I've seen: If you want to know the final temperature of an object that travels through a ...
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Zeta regularization of Infinite product

I was trying to compute the product $$ P_{a,b} = \prod_{n=1}^\infty(an + b), $$ after I computed $$ P_{1,b} = \prod_{n=1}^\infty(n + b) = \frac{\sqrt{2\pi}}{\Gamma(b+1)}, $$ and the well-known $$...
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Evaluating path integral

I am having some trouble remembering how to evaluate path integrals involving multiple particles. Suppose that I have two interacting particles with Lagrangian $$L= \frac{1}{2}m \dot y^2-\frac{1}{2}m ...
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free energy in the path integral equivalent to the classical 1D Ising model: Shankar

In chapter 21 (eqtn 21.2.90) Shankar gives the free energy (of the PI problem equivalent to the classical 1D Ising model), $$ f=-E_0 = K^* $$ I dont understand how he arrives at this considering in ...
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Anomalous Slavnov-Taylor identity

I will be happy if someone could clarify the mystery here. Consider the following derivation of the anomalous Slavnov-Identity. It's based on lecture notes by Adel Bilal. Suppose we have an action ...
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Quantum Anomalies and Quantum Symmetries

In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be ...
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Chern Simons Theory over S^3 as integral - what is domain of integration?

I found these nice lecture notes Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories so I am hoping to understand some parts of the Chern Simons theory better. ...
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75 views

Coherent state path integral - derivation

I divided the time interval $[t_0=:t_i,t_f:=t_N]$ into $N$ steps $[t_{k-1},t_{k}],\, k=1,\dots, N$ and applied the resolution of unity for coherent states \begin{equation} \mathbb{I}=\int_\mathbb{C}\...
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Free space propagator: reconciling two results

In quantum mechanics, the free space propagator $G(q_f=0,q_i=0;\tau)$ can be easily calculated to be $$\sqrt{\frac{m}{2\pi i \hbar \tau}}$$ by inserting an identity operator. However if we use ...
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Making mathematical sense on a Feynman's path integral equation

Usually we find this relation in the context of Feynman's path integral (see, for example, Maggiore's book on QFT, pg 223): $ \int_{q_i}^{q_f}[dq] = \int_{-\infty}^{\infty}d\bar{q}\int_{q_i}^{\bar q}[...
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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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185 views

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 ...