Skip to main content

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.

Filter by
Sorted by
Tagged with
-2 votes
0 answers
44 views

$i\epsilon$ prescription for finite systems [closed]

What is physical interpretation of path integral for finite time and finite epsilon (i.e without taking limits time->+-inf, epsilon->0)? Does it mean you are doing some finite temperature qft ...
Peter's user avatar
  • 343
1 vote
0 answers
45 views

Coulomb gas correlators on the sphere

I am trying to understand Appendix B.2 of Nakayama's notes (https://arxiv.org/abs/hep-th/0402009), wherein he derives the correlation functions of the following action (Coulomb gas) on the sphere: $$ ...
Jay Padayasi's user avatar
1 vote
1 answer
54 views

Time evolution of operators in the path integral formalism

I have studied the Hamiltonian formulation of non-relativistic quantum mechanics (NRQM) in detail but have limited knowledge of the path integral formulation. In the interaction picture of the ...
SCh's user avatar
  • 756
2 votes
1 answer
87 views

What is the physical meaning of the normalization of the propagator in quantum mechanics?

Suppose we have a quantum field theory (QFT) for a scalar field $\phi$ with vacuum state $|\Omega\rangle$. Then, in units where $\hbar = 1$, we postulate that the vacuum expectation value (VEV) of any ...
zeroknowledgeprover's user avatar
0 votes
1 answer
54 views

Why isn't the free particle particle a function of the absolute value of the difference of the time?

The one-dimensional free particle Lagrangian is given by $$ \mathcal{L} = \frac{m}{2}\dot x^2. $$ Since the Lagrangian is translation-invariant, one usually argues that the propagator can only be a ...
zeroknowledgeprover's user avatar
2 votes
2 answers
81 views

How does inserting an operator in the path integral change the equation of motion?

I am reading this review paper "Introduction to Generalized Global Symmetries in QFT and Particle Physics". In equation (2.43)-(2.47), the paper tried to prove that when $$U_g(\Sigma_2)=\exp\...
gshxd's user avatar
  • 133
2 votes
1 answer
107 views

Derivation of Schrödinger equation in Feynman-Hibbs

I am going through the derivation in chapter 4-1 of "Quantum Mechanics and Path Integrals. Emended Edition" by Feynman and Hibbs. The chapter starts with a proof of the equivalence of the ...
Emilia's user avatar
  • 131
3 votes
3 answers
609 views

Path integral at large time

From the path integral of a QFT: $$Z=\int D\phi e^{-S[\phi]}$$ What is a nice argument to say that when we study the theory at large time $T$, this behaves as: $$ Z \to e^{-TE_0} $$ where $E_0$ is the ...
BVquantization's user avatar
1 vote
1 answer
146 views

2PI Effective Action from Double Legendre Transformation

This answer (https://physics.stackexchange.com/q/348673) provides good intuition for why Legendre transformation induces 1-particle irreducible graphs: It mainly tries to convey the idea that the ...
JinH's user avatar
  • 126
0 votes
0 answers
49 views

Question about Path Integrals and Exchange Statistics in Steve Simon's "Topological Quantum"

In the introduction to the path integral approach leading to exchange statistics for many particles, Steve Simon breaks up the sum of paths into two types: paths where particles do not exchange (type ...
SAlvi's user avatar
  • 19
1 vote
0 answers
76 views

physical interpratation of partition function in Quantym field theory

Partition function in Statistical mechanics is given by $$ Z = \sum_ne^{-\beta E_n} $$ For QFT, it is defined in terms of a path integral: $$ Z = \int D\phi e^{-S[\phi]} $$ How can we see the relation ...
BVquantization's user avatar
2 votes
1 answer
49 views

A Limited Sense of Path Integral Respecting Classical EOM

In Weinberg QFT V1, we got the general path integral of time-ordered operators product, equation (9.1.38), $$\langle{q',t'|\text{T}\left\{\mathcal{O}_A\left(P(t_A),Q(t_A)\right)\mathcal{O}_B\left(P(...
Ting-Kai Hsu's user avatar
0 votes
1 answer
39 views

Trace formula for fermionic variables

I am using Bravyi's paper "Lagrangian representation of fermionic linear optics" and one formula that stumbled me is the trace formula in Eq. (15) in the picture below: I do not see how to ...
Evangeline A. K. McDowell's user avatar
2 votes
1 answer
92 views

Understanding the Gaussian weight and the parameter $\xi$ when quantizing gauge theories

In section 9.4 of Peskin & Schroeder's textbook on quantum field theory, when applying the Faddeev Popov procedure to quantize an Abelian gauge theory, they obtain the following functional ...
CBBAM's user avatar
  • 3,350
0 votes
1 answer
75 views

Path integral in field theory

I cannot understand the connection between the Grassmann variable and fermion in the derivation of path integral. I well understood the definition of an integral over a Grassmann variable but I still ...
roberto's user avatar
  • 71
0 votes
0 answers
48 views

Derivation of measure for summation over surfaces, including the polyakov action

In his 1981 paper "Quantum geometry of bosonic strings" Polyakov defines a measure for the summation over continuous surfaces. This measure must count all surfaces of a given area with the ...
Jens Wagemaker's user avatar
2 votes
2 answers
77 views

Time ordering for a time-dependent Hamiltonian in Path integral derivation

I am currently taking a class on Quantum Field Theory. The propagator was defined as: $$K(x,t;x',t') = \langle x|\hat{T}e^{{\frac{-i}{\hbar}\int_{t}^{t'}dtH(t)}}|x\rangle$$ where, $\hat{T}$ is the ...
ofbrackets's user avatar
1 vote
0 answers
90 views

In the path integral formulation of QFT, how do we get quantized particles out of a field?

Every QFT textbook starts by basically postulating that we have discrete states connected by creation and annihilation operators. In Quantum Mechanics, we started from a differential equation and ...
A. Kriegman's user avatar
  • 1,262
2 votes
1 answer
83 views

Topological behavior (or asymptotics at infinity) of gauge fields assumed in Fujikawa method

Chiral anomaly is computed very elegantly by Fujikawa method, which is also presented in Section 22.2 of Weinberg QFT textbook volume 2 or wikipedia. Here, the underlying spacetime is assumed to be $\...
Keith's user avatar
  • 1,669
1 vote
2 answers
55 views

Infrared regularizing the harmonic oscillator path integral

This is from Laine and Vuorinen’s Basics of Thermal Field Theory. I do not understand why the fact that the integral over $x(\tau)$ implies the following regularization scheme. That is, I don’t ...
Vimal Rajan's user avatar
0 votes
1 answer
122 views

Fourier transform of the Gaussian action for the real scalar bosonic field

In my current homework, we have to get familiar with quadratic theory in order to reach $\phi^4$-theory. So the starting point is $$Z = \int Dx e^{-S[\phi]}$$ with the action for the real scalar ...
Johnny_T's user avatar
0 votes
1 answer
62 views

Chern-Simons theory: Connection between Thermal and Quantum Partition Function

I have been reading the Quantum Hall Effect from Prof. David Tong's notes. In the section on Chern-Simons theory, he describes the connection between the Thermal Partition Function and the Quantum ...
harshit_'s user avatar
2 votes
1 answer
71 views

Free scalar field deriving Ehrenfest using the path integral

In his lecture notes on String theory, David Tong derives Ehrenfest theorem using the path integral: $$S = \frac{1}{4\pi \alpha'}\int d^2\sigma\ \partial_\alpha X\ \partial^\alpha X\tag{4.19}$$ $$ 0 =...
Jens Wagemaker's user avatar
5 votes
1 answer
114 views

How important are purely imaginary finite action solutions for first-order instanton contributions?

I am working on a physics problem where I have to calculate instanton contributions for a non-relativistic Hamiltonian $$H=-\frac{1}{2}\frac{d^2}{dx^2}+\frac{1}{2}x^2+\frac{1}{6}g^2x^6 \tag 1$$ for ...
Young Plato's user avatar
1 vote
1 answer
101 views

What's the minima of the quantum effective action?

Consider the vacuum expectation value of a (for simplicity scalar) field $\phi$, we know that its vacuum expectation value can be expressed as $$\langle\phi\rangle=\frac{1}{\mathcal{Z}}∫\mathcal{D}\...
Filippo's user avatar
  • 477
1 vote
0 answers
76 views

Majorana Boson Coherent States

Consider $a$ be a bosonic operator, and we define $\Phi = a+a^{\dagger}$ and it is clear that $\Phi^{\dagger}=\Phi$ that implies "Majorana Boson". Now, i want to find the coherent states for ...
Santanu Singh's user avatar
2 votes
3 answers
112 views

How do vacuum bubbles "dress" terms in the $S$-matrix numerator?

I am self-studying QFT using the book "A modern introduction to quantum field theory" by Maggiore. On page 124-125 he's doing the calculation in the interaction picture for a process with ...
Andrea's user avatar
  • 613
2 votes
1 answer
96 views

The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT

I'm reading Vol. 2 of Weinberg's QFT. As what I learnt from both P&S and Weinberg, the generating function is defined as $$ Z[J] = \int \mathcal{D}\phi \exp(iS_{\text{F}}[\phi] + i\int d^4x\phi(x) ...
LaplaceSpell's user avatar
1 vote
1 answer
49 views

Fermionic propagator [closed]

Given the fermionic generating functional $$Z[\eta]=\ det^{\frac{1}{2}}(K_{ij})e^{-\frac{i}{2}\eta_{i}G^{ij}\eta_{j}},\tag{1}$$ where $$G^{ij}=K^{-1}_{ij}$$ is the Green function of our theory, then ...
Michael 's user avatar
0 votes
1 answer
124 views

The definition of the path integral

I still have big conceptual questions about the path integral. According to (24.6) of the book "QFT for the gifted amateur" from Lancaster & Blundell the path integral is equal to $$Z =\...
Frederic Thomas's user avatar
3 votes
0 answers
103 views

What are exactly the loop correction to the potential? [duplicate]

I am struggling with the concept of quantum effective action, but first recall the definition : given a Wilsonian effective action $W[J]$ of our theory, the quantum effective action is just $$\Gamma[\...
Filippo's user avatar
  • 477
1 vote
0 answers
67 views

Derivation of massive photon propagator

I'm trying to derive the massive photon propagator using the path integral formalism for a theory with $$ \mathcal{L} = -\dfrac{1}{4} F_{\mu\nu} F^{\mu\nu} + \dfrac{1}{2} m^2 A_\mu A^\nu, \text{with } ...
Gabriel Ybarra Marcaida's user avatar
2 votes
1 answer
98 views

Proof of Batalin-Fradkin-Vilkovisky (BFV) theorem using BRST operator and graded Poisson bracket algebra

In the proof of Batalin-Fradkin-Vilkovisky (BFV) theorem one has to determine how the path integral measure changes. The set of canonical variables $$\varphi = (Q^A;P_{A}) =(q,\eta;\pi,\mathscr{P})\...
Faber Bosch's user avatar
0 votes
1 answer
48 views

Can any meaning be given to a path integral with no fixed end point?

A path integral has the interpreted as the probability a particle goes from $A$ to $B$ in time $t$. Such a path integral is given by $$\langle x_B, t|x_A, 0\rangle = \frac{1}{Z} \int_{\textrm{paths } ...
CBBAM's user avatar
  • 3,350
5 votes
1 answer
78 views

Onsager-Machlup functional and the Boltzmann distribution

I've been looking into path integral representations of stochastic processes lately and came across the Onsager-Machlup functional description of the Langevin equation. In the overdamped case, where ...
aQuarkyName's user avatar
1 vote
2 answers
126 views

Why does a singularity imply the need for a distribution?

I am following Section 11 of Prof. Etingof's MIT OpenCourseWare notes on "Geometry And Quantum Field Theory" in which he says: ...for $d = 1$, the Green's function $G(x)$ is continuous at $...
CBBAM's user avatar
  • 3,350
1 vote
1 answer
88 views

Problem solving for Wilsonian Effective Action

I'm currently doing some basic questions on renormalisation group, but I've ran into a wall when it comes to one particular step in an answer. The question is as follows: This problem is a toy model ...
Aidan's user avatar
  • 90
1 vote
1 answer
92 views

Does path intergral formula only works in perturbative situation?

I'm learning quantum field theory. In Peskin & Schroeder, when they derive $$\int {D\phi(x)\phi ({x_1})\phi ({x_2})\exp [i\int {{d^4}x\mathcal{L(x)}] = \left\langle {{\phi _b}|{e^{ - iHT}}T\{ \phi ...
Errorbar's user avatar
  • 368
4 votes
2 answers
672 views

Ghosts in QCD Lagrangian

The QCD Lagrangian is $$ \mathcal{L}_{\text{QCD}} = -\dfrac{1}{2} \text{Tr}\, G_{\mu\nu}G^{\mu\nu} + \sum_i^{N_f} \bar{q_i} \left(i \gamma^\mu \mathcal{D}_\mu - m_i\right)\,q_i, \tag{1} $$ where $\...
Gabriel Ybarra Marcaida's user avatar
0 votes
0 answers
47 views

How to derive the gauge invariance of Yang-Mills action with external source?

In the Faddeev-Popov procedure of path integral of $$ Z[J] = \int [DA] e^{iS(A,J)}, \quad S(A,J)= \int d^4x [-\frac{1}{4}F^{a\mu\nu}F_{a\mu\nu} + J^{a\mu}A_{a\mu} ] $$ we have used that $S(A,J)$ is ...
zixuan feng's user avatar
2 votes
0 answers
37 views

Does a quantum field theory have an effective single-particle action in the single-particle subspace?

In non-interacting quantum field theories, the particle number is conserved so we can restrict to a given subspace of fixed particle number. On the single-particle subspace, the state will evolve ...
Hermitian_hermit's user avatar
7 votes
1 answer
663 views

What happens to branching in the Many-Worlds Interpretation of quantum mechanics in the limit when Planck's constant goes to 0?

We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why ...
Guillaume Laporte's user avatar
1 vote
1 answer
67 views

Time ordered correlator from path integral: equation of motion?

Consider a Lagrangian $L(\phi)$ for a field $\phi$ (assume it is a free real scalar for simplicity). Then the time ordered propagator can be expressed as a path integral $$ \langle\Omega|T\{ \phi(x) \...
QuantumEyedea's user avatar
0 votes
0 answers
26 views

Resources for Faddeev-Popov method. (Specifically for diffeomorphism gauge fixing.)

I am struggling to get the same result as this paper (eq. 3.10) for my ghost field when gauge-fixing diffeomorphisms in linearized gravity. I would appreciate it if someone could point me in the ...
0 votes
1 answer
95 views

In QFT when performing path integral, why don’t we divide it by the volume of Poincaré group, as what we did for gauge group?

When performing path integral in gauge theory, we naively want to compute $$ Z = \int DA \exp(iS[A]) $$ But we noticed, that because the action is the same for gauge equivalent conditions, we should ...
zixuan feng's user avatar
0 votes
0 answers
39 views

What does it even mean?: "Perturbation theory developed around minima of potential (vacuum) is stable."

(Context: QFT, spontaneous symmetry breaking): What I have understood from reading the path integral version of the story is that this "vacuum" is actually the classical solution [i.e. which ...
nmnphy's user avatar
  • 11
3 votes
2 answers
127 views

Instantons and Spontaneous Symmetry Breaking

I'm following an introductory lecture on instantons by Hilmar Forkel. In a non-relativistic quantum mechanical setting we have the potential $$ V(x) = \dfrac{\alpha^2 m}{2 x_0^2} (x^2 - x_0^2)^2 \tag{...
Gabriel Ybarra Marcaida's user avatar
4 votes
1 answer
72 views

How does path integral quantization ensure unitarity?

Unitarity can be verified post hoc by examining the optical theorem. In the context of path integral quantization where formal derivation starting from canonical quantization is unavailable, is it ...
Bababeluma's user avatar
2 votes
0 answers
71 views

Why is it valid to only consider linear-order gauge transformation when quantizing non-Abelian gauge theory?

To quantize the non-Abelien gauge theory. We multiply the path integral by: $f[A]=\int \mathcal{D}\pi exp[-i\int d^4 x {1\over \xi}(\partial_\mu D_\mu \pi^a)^2]$ then we can shift the argument in the ...
Bababeluma's user avatar
2 votes
1 answer
60 views

Expanding the generating functional $W[J]$ for connected diagrams as a power series in $\hbar$

This is a follow up of a recent post I made (Making sense of stationary phase method for the path integral), but here I will work in Euclidean space, i.e. a Wick rotation has been performed. Let $$Z[J]...
CBBAM's user avatar
  • 3,350

1
2 3 4 5
32