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Question 1

2votes

1answer

201views

What is the point of the "Polarization Insertion" in many-body theory?

In Fetter and Walecka's Quantum Theory of Many-Particle Systems, after a discussion of Dyson's equation for the single particle Green's function in spacetime ($x$) and momentum/frequency ($k$; for ...

frobenius

159

askedNov 20 at 3:35

Question 2

1vote

0answers

93views

Dyson series expression for the two-point Green function

On Chapter 7 of Fetter & Walecka, the authors prove Dyson formula for the (imaginary time) propagator $U(t,t_{0}) = e^{H_{0}t_{0}}e^{-H(t_{0}-t)}e^{-H_{0}t}$, where I am ommitting the $\hbar$'s. ...

InMathweTrust

251

askedNov 19 at 8:33

Question 3

6votes

1answer

263views

Why do these first-order diagrams represent "direct" and "exchange" interactions?

In Quantum Theory of Many Particle Systems by Fetter and Walecka, they perturbatively expand the fermionic interacting single particle Green's function $iG_{\alpha\beta}(x, y)$ (where $\alpha$, $\beta$...

frobenius

159

askedNov 15 at 21:56

Question 4

1vote

1answer

92views

Understanding how second quantization recovers full $N$-body correlations from classical Schrödinger fields

I'm trying to understand a conceptual point in many-body quantum mechanics and quantum field theory.Starting point: Consider a classical Schrödinger field $\psi(\mathbf r, t)$ with interactions, ...

Michiel

310

askedNov 14 at 10:59

Question 5

0votes

1answer

71views

Confused about the Kinetic Energies of a many-body system

My Question stems from the following problem:Consider two resting Point Masses, each with mass $m$, which are connected (the connection having no mass). A Force $F$, which is always perpendicular to ...

entiges_Enton

87

askedNov 13 at 16:01

Question 6

0votes

0answers

80views

What does it mean to do second quantization in a correlated many body system and how does this relate to Green's functions?

In standard second quantization for a many body system you write out a Fock state $|n_1, n_2,..., n_M\rangle$ (supposing there are $M$ independent particle states $|\psi_i\rangle$). Now this works ...

Physics_Boss_India

133

askedNov 7 at 22:55

Question 7

1vote

0answers

49views

Greens function in Many Body Physics [duplicate]

What is the physical intuition for retarded many body greens function$$G^{R}(rt,rt')=-i\theta(t-t')\langle[\hat{\psi}(rt),\hat{\psi}^{\dagger}(r't')]\rangle$$where the square bracket stands for ...

Ranbir Barman

11

askedNov 3 at 11:49

Question 8

1vote

0answers

56views

Is particle number a monotonic function of chemical potential when fixing self-energy?

I am performing numerical calculations using quantum many-body theory, and I would like to fix the particle number, either for fermions or bosons. The particle number can be expressed in terms of the ...

Black Monolith

763

askedOct 30 at 16:38

Question 9

5votes

1answer

191views

Effective interactions and screening from Feynman diagrams in condensed matter and interpretations

recently I was revisiting the path integral formalism to approach condensed matter systems, and there is a question I've always had which is not yet clear to me.In physics, there are many ways to ...

Eduardo Sánchez

91

askedOct 29 at 10:32

Question 10

9votes

4answers

1kviews

What is the meaning of "knowing all the Green functions implies knowledge of the full theory"?

I have encountered many times the sentence in the title. Either written in books or told by more experienced friends, there seems to be a consensus that "If we know all Green functions of a ...

InMathweTrust

251

askedOct 14 at 8:46

Question 11

4votes

1answer

124views

Contour Integral in Friedel oscillation calculation

In Section 14 of Fetter&Walecka's Quantum Theory of Many-Particle Systems, the authors evaluate the induced charge density due to a static charge impurity:$$\delta \langle \rho(\mathbf{x}) \...

Jason Chen

747

askedOct 4 at 4:08

Question 12

4votes

0answers

78views

Connection between anti-resonant $|vc⟩$ -$|c'v'⟩$ terms in Bethe-Salpeter Equation (BSE) and plasmonic excitations

I’m studying the Bethe–Salpeter Equation (BSE) and I understand that in the full (non-Tamm-Dancoff Approximated) BSE there are anti-resonant coupling terms connecting$|vc\rangle$ and $|c'v'\rangle$ ...

pter26

205

askedOct 2 at 15:47

Question 13

5votes

3answers

817views

Making sense of perturbation theory in many-body physics

I am trying to teach myself perturbation theory in the context of many-body quantum mechanics. I must say I am facing some difficulties in understanding the motivations and ideas behind the method, ...

MathMath

1,377

askedSep 28 at 16:26

Question 14

2votes

1answer

144views

Understanding frequency and frequency integration of Green's function

The single particle Green's function is defined by:$$G(\mathbf{k}, t) = \langle \Psi | \mathcal{T} c_{\mathbf{k}}(t) c_{\mathbf{k}}^{\dagger}(0) | \Psi \rangle$$The physical intuition behind this ...

Jason Chen

747

askedSep 23 at 11:22

Question 15

2votes

1answer

170views

How do we canonically describe the Hilbert space of two different species of spinless fermions? [duplicate]

I am trying to understand the canonical purification isomorphism for fermionic systems described in Quantum epidomology and more specifically in Spread of entanglement in SYK chain (sec 2.2).My ...

jrobins

127

askedSep 7 at 12:17

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Stack Exchange Network

Questions tagged [many-body]

What is the point of the "Polarization Insertion" in many-body theory?

Dyson series expression for the two-point Green function

Why do these first-order diagrams represent "direct" and "exchange" interactions?

Understanding how second quantization recovers full $N$-body correlations from classical Schrödinger fields

Confused about the Kinetic Energies of a many-body system

What does it mean to do second quantization in a correlated many body system and how does this relate to Green's functions?

Greens function in Many Body Physics [duplicate]

Is particle number a monotonic function of chemical potential when fixing self-energy?

Effective interactions and screening from Feynman diagrams in condensed matter and interpretations

What is the meaning of "knowing all the Green functions implies knowledge of the full theory"?

Contour Integral in Friedel oscillation calculation

Connection between anti-resonant $|vc⟩$ -$|c'v'⟩$ terms in Bethe-Salpeter Equation (BSE) and plasmonic excitations

Making sense of perturbation theory in many-body physics

Understanding frequency and frequency integration of Green's function

How do we canonically describe the Hilbert space of two different species of spinless fermions? [duplicate]

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