scholarly journals Spin structures and baby universes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Arjun Kar ◽  
Simon F. Ross ◽  
Tomonori Ugajin
Keyword(s):  
Hilbert Space ◽  
Path Integral ◽  
Spin Structure ◽  
Partition Functions ◽  
Unitary Theory ◽  
Spin Structures ◽  
Dual Interpretation ◽  
Baby Universes ◽  
Creation Operators ◽  
Baby Universe

Abstract We extend a 2d topological model of the gravitational path integral to include sums over spin structure, corresponding to Neveu-Schwarz (NS) or Ramond (R) boundary conditions for fermions. This path integral corresponds to a correlator of boundary creation operators on a non-trivial baby universe Hilbert space, and vanishes when the number of R boundaries is odd. This vanishing implies a non-factorization of the correlator, which necessitates a dual interpretation of the bulk path integral in terms of a product of partition functions (associated to NS boundaries) and Witten indices (associated to R boundaries), averaged over an ensemble of theories with varying Hilbert space dimension and different numbers of bosonic and fermionic states. We also consider a model with End-of-the-World (EOW) branes, for which the dual ensemble then includes a sum over randomly chosen fermionic and bosonic states. We propose two modifications of the bulk path integral which restore an interpretation in a single dual theory: (i) a geometric prescription where we add extra boundaries with a sum over their spin structures, and (ii) an algebraic prescription involving “spacetime D-branes”. We extend our ideas to Jackiw-Teitelboim gravity, and propose a dual description of a single unitary theory with spin structure in a system with eigenbranes.

TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION

2013 ◽  
Vol 12 (04) ◽  
pp. 1350026 ◽  
Author(s):  
MARCIN BUCHOWIECKI
Keyword(s):  
Monte Carlo ◽  
Temperature Dependence ◽  
Equilibrium Constant ◽  
Path Integral ◽  
Thermodynamic Integration ◽  
Partition Functions ◽  
Integration Path ◽  
Path Integral Monte Carlo

The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).

scholarly journals Construction and pure infiniteness of $C^*$-algebras associated with lambda-graph systems

2005 ◽  
Vol 97 (1) ◽  
pp. 73 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Hilbert Space ◽  
Bratteli Diagram ◽  
C Algebra ◽  
C Algebras ◽  
Shift Transformation ◽  
Labeled Graphs ◽  
Graph System ◽  
Creation Operators

A $\lambda$-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [16] the author has introduced a $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ associated with a $\lambda$-graph system $\mathfrak{L}$ by using groupoid method as a generalization of the Cuntz-Krieger algebras. In this paper, we concretely construct the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ by using both creation operators and projections on a sub Fock Hilbert space associated with $\mathfrak{L}$. We also introduce a new irreducible condition on $\mathfrak{L}$ under which the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ becomes simple and purely infinite.

scholarly journals Wormhole calculus, replicas, and entropies

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Steven B. Giddings ◽  
Gustavo J. Turiaci
Keyword(s):  
Black Hole ◽  
Probability Distributions ◽  
Information Loss ◽  
Coupling Constants ◽  
Quantum Mechanical ◽  
Standard Description ◽  
Standard Quantum ◽  
Black Hole Information ◽  
Baby Universes ◽  
Baby Universe

Abstract We investigate contributions of spacetime wormholes, describing baby universe emission and absorption, to calculations of entropies and correlation functions, for example those based on the replica method. We find that the rules of the “wormhole calculus”, developed in the 1980s, together with standard quantum mechanical prescriptions for computing entropies and correlators, imply definite rules for limited patterns of connection between replica factors in simple calculations. These results stand in contrast with assumptions that all topologies connecting replicas should be summed over, and call into question the explanation for the latter. In a “free” approximation baby universes introduce probability distributions for coupling constants, and we review and extend arguments that successive experiments in a “parent” universe increasingly precisely fix such couplings, resulting in ultimately pure evolution. Once this has happened, the nontrivial question remains of how topology-changing effects can modify the standard description of black hole information loss.

STATIONARY PHASE, QUANTUM MECHANICS AND SEMI-CLASSICAL LIMIT

1996 ◽  
Vol 08 (08) ◽  
pp. 1161-1185 ◽  
Author(s):  
JORGE REZENDE
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Stationary Phase ◽  
Finite Number ◽  
Path Integral ◽  
Critical Points ◽  
Classical Limit ◽  
Oscillatory Integral ◽  
Feynman Path Integral ◽  
Feynman Path

A method of stationary phase for the normalized-oscillatory integral on Hilbert space is developed in the case where the phase function has a finite number of critical points which are non-degenerate. Applications to the Feynman path integral and the semi-classical limit of quantum mechanics are given.

PARTITION FUNCTIONS OF THE SUPERCONFORMAL GHOST THIRRING MODEL

1989 ◽  
Vol 04 (20) ◽  
pp. 5553-5574 ◽  
Author(s):  
D. Z. FREEDMAN ◽  
K. PILCH
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Formal Series ◽  
Open String ◽  
Integral Representations ◽  
Thirring Model ◽  
Partition Functions ◽  
First Order ◽  
Integral Methods ◽  
The One

The one-loop partition functions of the superconformal Thirring model for first order b − c and β − γ ghost fields are studied for both closed and open string boundary conditions. Bosonized partition functions are given by formal series which usually diverge because the energy spectrum of the theory is unbounded below as a correlate of nonunitarity. However, the same partition functions are then calculated by path integral methods directly in the fermionic formulation, and well-defined (convergent) integral representations are obtained. A formal series expansion of those integrals reproduces the bosonized partition functions.

GEOMETRIC STRUCTURES IN PHYSICS

2012 ◽  
Vol 09 (02) ◽  
pp. 1260026 ◽  
Author(s):  
L. J. BOYA
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Mechanics ◽  
Path Integral ◽  
Riemannian Manifolds ◽  
Symplectic Geometry ◽  
Gauge Theories ◽  
Classical Mechanics ◽  
The Past ◽  
Modern Physics

Geometry and Physics developed independently, until the past twentieth century, where physicists realized geometry is rather flexible and can adapt itself to the needs and characteristics of modern physics. Besides the use of Riemannian manifolds to describe General Relativity, classical mechanics encounters symplectic geometry, not to speak of the bundle connection ingredient of modern gauge theories; even Quantum Mechanics, after the initial Hilbert space period, is seeking nowadays to adapt itself better to a geometrical interpretation, by imperatives of the path integral description and also to incorporate more clearly the symplectic aspects of its classical antecedent.

A Theoretical Approach to Selection of a Biologically Active Substance in Ultra-Low Doses for Effective Action on a Biological System

Homeopathy ◽  
2018 ◽  
Vol 107 (02) ◽  
pp. 137-142 ◽  
Author(s):  
Liudmila Boldyreva
Keyword(s):  
Effective Action ◽  
Biological System ◽  
Spin Structure ◽  
Biologically Active ◽  
Precession Frequency ◽  
Magnetic Vector Potential ◽  
Low Doses ◽  
Spin Structures ◽  
Virtual Particles ◽  
Spin Flip

Background and Aim An approach is offered to selecting a biologically active substance (BAS) in ultra-low dose for effective action on a biological system (BS). The technique is based on the assumption that BAS in ultra-low doses exerts action on BS by means of spin supercurrent emerging between the spin structure created by BAS, on the one hand, and the spin structure created by BS, on the other hand. According to modern quantum-mechanical concepts, these spin structures may be virtual particles pairs having precessing spin (that is, be essentially spin vortices in the physical vacuum) and created by the quantum entities that BAS and BS consist of. The action is effective provided there is equality of precession frequencies of spins in these spin structures. Method In this work, some methods are considered for determining the precession frequencies of spins in virtual particles pairs: (1) determination of energy levels of quantum entities that BS and BAS consist of; (2) the use of spin-flip effect of the virtual particles pair spin, the effect being initiated by action of magnetic vector potential (the spin-flip effect takes place when the varied frequency of the magnetic vector potential equals the precession frequency of the spin); (3) determining the frequencies of photons effectively acting on BS. Results and Conclusion It is shown that the effect of BAS in ultra-low doses on BS can be replaced by the effect of a beam of low-intensity photons, if the frequency of photons equals the precession frequency of spin in spin structures created by BS. Consequently, the color of bodies placed near a biological system is able to exert an effective action on the biological system: that is “color therapy” is possible. It is also supposed that the spin-flip effect may be used not only for determining the precession frequency of spin in spin structures created by BS but also for therapeutic action on biological systems.

scholarly journals PATH INTEGRAL REPRESENTATION FOR INTERFACE STATES OF THE ANISOTROPIC HEISENBERG MODEL

2000 ◽  
Vol 12 (10) ◽  
pp. 1325-1344 ◽  
Author(s):  
OSCAR BOLINA ◽  
PIERLUIGI CONTUCCI ◽  
BRUNO NACHTERGAELE
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Two Dimensions ◽  
Integral Model ◽  
Partition Functions ◽  
Translation Invariant ◽  
Xxz Model ◽  
Path Integral Representation ◽  
Ferromagnetic Chain ◽  
The One

We develop a geometric representation for the ground state of the spin-1/2 quantum XXZ ferromagnetic chain in terms of suitably weighted random walks in a two-dimensional lattice. The path integral model so obtained admits a genuine classical statistical mechanics interpretation with a translation invariant Hamiltonian. This new representation is used to study the interface ground states of the XXZ model. We prove that the probability of having a number of down spins in the up phase decays exponentially with the sum of their distances to the interface plus the square of the number of down spins. As an application of this bound, we prove that the total third component of the spin in a large interval of even length centered on the interface does not fluctuate, i.e. has zero variance. We also show how to construct a path integral representation in higher dimensions and obtain a reduction formula for the partition functions in two dimensions in terms of the partition function of the one-dimensional model.

Sign in / Sign up

Export Citation Format

Share Document