From conformal quantum mechanics on bordered Riemann surfaces to covariant string field theory

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

Download Full-text

QLB for Quantum Many-Body and Quantum Field Theory

10.1093/oso/9780199592357.003.0033 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Mechanics ◽

Quantum Computing ◽

Single Particle ◽

Body Problem ◽

Three Dimensions ◽

Quantum Field ◽

Many Body ◽

Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

Download Full-text

Unoriented Open-Closed String Field Theory*

Progress of Theoretical Physics Supplement ◽

10.1143/ptps.134.137 ◽

1999 ◽

Vol 134 ◽

pp. 137-152

Author(s):

Taichiro Kugo

Keyword(s):

Field Theory ◽

String Field Theory ◽

Closed String

Download Full-text

Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics

Entropy ◽

10.3390/e23010125 ◽

2021 ◽

Vol 23 (1) ◽

pp. 125

Author(s):

Tobias Gulden ◽

Alex Kamenev

Keyword(s):

Quantum Mechanics ◽

Algebraic Topology ◽

Riemann Surfaces ◽

Surrounding Medium ◽

Coulomb Systems ◽

Dielectric Constants ◽

Ion Interactions ◽

Multivalent Ions ◽

Electric Filed ◽

Entropic Effects

We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.

Download Full-text