Quantum-classical correspondence via coherent state in integrable field theory

Sato, Jun; Yumibayashi, Tsukasa

doi:10.48550/arxiv.1811.03186

Cited by 4 publications

(3 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a classical theory, a soliton is a solution of the classical equations of motion with certain properties. In a quantum theory, in the weak coupling limit, it is a coherent state defined entirely in terms of that classical solution [1,2]. At small but finite coupling, solitons can be described by a semiclassical expansion about this coherent state [3].…”

Section: Introductionmentioning

confidence: 99%

Constructing Quantum Soliton States Despite Zero Modes

Evslin¹

2020

Preprint

View full text Add to dashboard Cite

In classical Lorentz-invariant field theories, localized soliton solutions necessarily break translation symmetry. In the corresponding quantum field theories, the position is quantized and, if the theory is not compactified, they have continuous spectra. It has long been appreciated that ordinary perturbation theory is not applicable to continuum states. Here we argue that, as the Hamiltonian and momentum operators commute, the soliton ground state can nonetheless be found in perturbation theory if one first imposes that the total momentum vanishes. As an illustration, we find the subleading quantum correction to the ground state of the Sine-Gordon soliton.

show abstract

Section: Introductionmentioning

confidence: 99%

Constructing Quantum Soliton States Despite Zero Modes

Evslin¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…This perturbation theory is simplest when the Hamiltonian is normal ordered, so that all a † p appear to the left of all a p . At the same leading order 1 , the ground state of a quantum soliton is given by a coherent state formed by shifting the fields by the functions corresponding to their classical solutions [3,4,5]. The normal modes of the quantum soliton are, at linear order, described by quantum harmonic oscillators.…”

Section: Introductionmentioning

confidence: 99%

Normal Ordering Normal Modes

Evslin

2020

Preprint

View full text Add to dashboard Cite

In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have vanishing expectation values in the one-loop soliton ground state. The Hamiltonian of the theory, however, is usually normal ordered in the basis of operators which create plane waves. In this paper we find the Wick map between the two normal orderings. For concreteness, we restrict our attention to Schrodinger picture scalar fields in 1+1 dimensions, although we expect that our results readily generalize beyond this case. We find that plane wave ordered n-point functions of fields are sums of terms which factorize into j-point functions of zero modes, breather and continuum normal modes. We find a recursion formula in j and, for products of fields at the same point, we solve the recursion formula at all j.

show abstract

“…The observation that underlies this paper is that (1.2) is a unitary equivalence. More specifically, we construct a unitary operator D f which maps the vacuum sector to the kink sector [12,13]. We define the regularized kink sector Hamiltonian H by conjugating the defining, regularized vacuum-sector Hamiltonian H with this operator D f…”

Section: Jhep01(2023)073mentioning

confidence: 99%

Cut-off kinks

Evslin

Royston

Zhang

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

We answer the question: If a vacuum sector Hamiltonian is regularized by an energy cutoff, how is the one-kink sector Hamiltonian regularized? We find that it is not regularized by an energy cutoff, indeed normal modes of all energies are present in the kink Hamiltonian, but rather the decomposition of the field into normal mode operators yields coefficients which lie on a constrained surface that forces them to become small for energies above the cutoff. This explains the old observation that an energy cutoff of the kink Hamiltonian leads to an incorrect one-loop kink mass. To arrive at our conclusion, we impose that the regularized kink sector Hamiltonian is unitarily equivalent to the regularized vacuum sector Hamiltonian. This condition implies that the two regularized Hamiltonians have the same spectrum and so guarantees that the kink Hamiltonian yields the correct kink mass.

show abstract

Quantum-classical correspondence via coherent state in integrable field theory

Cited by 4 publications

References 12 publications

Constructing Quantum Soliton States Despite Zero Modes

Constructing Quantum Soliton States Despite Zero Modes

Normal Ordering Normal Modes

Cut-off kinks

Contact Info

Product

Resources

About