6
votes
0answers
47 views

Ambiguity in Asymptotic Perturbative Series and Instantons

I know there are a number of questions about the asymptoticity of perturbative series and about instantons on StackExchange (e.g. Instantons and Non Perturbative Amplitudes in Gravity from user566, ...
3
votes
1answer
99 views

Instanton in sine-Gordon equation

This is a statement from Giamarchi's book on Quantum Physics in 1D: "For a single-particle in a cosine potential, the slightest amount of tunneling between two cosine minima leads to conduction ...
4
votes
1answer
90 views

The relation between classical and quantum vacua

First let me clarify what I mean by vacuum. Suppose we are concerned with a theory of fields $\phi ^i$ defined on a stationary globally hyperbolic spacetime $M$ (I want the spacetime to be stationary ...
1
vote
0answers
28 views

Proof for the Mass gap of non-chiral Luttinger liquids with a Cosine potential

Similar to this post, I believe in condensed matter, people know the mass-gap statement for non-chiral Luttinger liquids with large $g \cos(\beta_{}^{} \cdot\phi_{})$ potential. This is the ...
1
vote
1answer
76 views

Euclidean functional Integrals

In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical approximation. To evaluate the ...
1
vote
0answers
75 views

Quantum tunneling in a time dependent potential

I wonder if I could use the technique for finding the tunneling rate given by $$ \Gamma=2 \Im[ F]$$ where $F$ is the free energy in case of time dependent potentials? Relevant to the previous ...
10
votes
1answer
304 views

The Origins of Instantons from Path Integrals

I know that you can come across non-perturbative effects in QFT, particular when the coupling constant lies outside the radius of convergence of the asympototic perturbation series. From the ...
1
vote
0answers
67 views

An Equality in The Calculus of Many Instantons

I am reading the review on instantons. When I tried to derive formula (2.27) on page 17, I always get the different coefficient of $gF_{mn}$ term. My calculation is just directly expanding the first ...
4
votes
1answer
134 views

Can massive fermions have zero modes?

I'm confused about fermion zero modes in relation to instantons. I understand that instantons can create fermion zero modes, but it's not clear to me when a fermion has a zero mode. For example, ...
5
votes
1answer
304 views

Yang-Mills instanton

How can instanton solution to Yang-Mills theory with gauge group $SU(3)$ or $SU(N)$ be obtained? For $SU(2)$ it is explained in textbooks but what about more general color gauge groups? EDIT: How ...
7
votes
1answer
111 views

Do instantons support quantum bound states?

When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...
6
votes
0answers
135 views

What is the rate of B violation expected in the standard model during high energy collisions?

In a recent question Can colliders detect B violation? I asked about detecting B violation in collisions. Here I am interested in the theory aspect. (I asked both questions originally in the same ...
12
votes
1answer
412 views

Instantons, anomalies, and 1-loop effects

A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way ...
7
votes
0answers
177 views

Instantons and Borel Resummation

As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
15
votes
1answer
136 views

Instantons and Non Perturbative Amplitudes in Gravity

In perturbative QFT in flat spacetime the perturbation expansion typically does not converge, and estimates of the large order behaviour of perturbative amplitudes reveals ambiguity of the ...