Download e-book for kindle: Path integrals, hyperbolic spaces, and Selberg trace by Christian Grosche

By Christian Grosche

During this moment variation, a accomplished assessment is given for direction integration in - and three-d (homogeneous) areas of continuing and non-constant curvature, together with an enumeration of all of the corresponding coordinate platforms which enable separation of variables within the Hamiltonian and within the direction essential. The corresponding direction vital ideas are provided as a tabulation. Proposals pertaining to interbasis expansions for spheroidal coordinate structures also are given. particularly, the instances of non-constant curvature Darboux areas are new during this variation.

the amount additionally includes effects at the numerical examine of the homes of a number of integrable billiard platforms in compact domain names (i.e. rectangles, parallelepipeds, circles and spheres) in - and third-dimensional flat and hyperbolic areas. particularly, the dialogue of integrable billiards in circles and spheres (flat and hyperbolic house) and in 3 dimensions are new compared to the 1st variation.

moreover, an outline is gifted on a few fresh achievements within the concept of the Selberg hint formulation on Riemann surfaces, its great generalization, their use in mathematical physics and string concept, and a few extra effects derived from the Selberg (super-) hint formula.

Show description

Read or Download Path integrals, hyperbolic spaces, and Selberg trace formulae PDF

Similar quantum theory books

Get A mathematical introduction to conformal field theory PDF

Half I supplies a close, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in dimensions. The conformal teams are made up our minds and the appearence of the Virasoro algebra within the context of the quantization of two-dimensional conformal symmetry is defined through the type of crucial extensions of Lie algebras and teams.

Read e-book online Uncommon paths in quantum physics PDF

Quantum mechanics is without doubt one of the so much attention-grabbing, and while such a lot arguable, branches of up to date technological know-how. Disputes have followed this technology for the reason that its start and feature now not ceased to today. unusual Paths in Quantum Physics permits the reader to consider deeply a few rules and strategies which are seldom met within the modern literature.

Read e-book online Mathematics of Quantization and Quantum Fields PDF

Unifying a variety of subject matters which are at present scattered through the literature, this booklet bargains a different and definitive evaluate of mathematical facets of quantization and quantum box conception. The authors current either simple and extra complicated issues of quantum box idea in a mathematically constant means, concentrating on canonical commutation and anti-commutation relatives.

Download e-book for iPad: Relativistische Quantenmechanik by Georg Wolschin (auth.)

Dieses Buch richtet sich an Studierende der Physik, die bereits über Grundkenntnisse der Quantenmechanik verfügen und relativistische Wellengleichungen kennenlernen möchten. Im Hauptteil des Buchs behandelt der Autor die Klein-Gordon-Gleichung und die Dirac-Gleichung, wobei er deren Bedeutung hervorhebt und auf interessante Anwendungen eingeht.

Additional info for Path integrals, hyperbolic spaces, and Selberg trace formulae

Example text

5 and 6 is to suggest the richness, flexibility and economy of texture available for solutions in a basis function approach. Next, we introduce the total invariant mass-squared M2 for the low-lying physical states in terms of a Hamiltonian H times a dimensionless integer for the total light-front momentum K M2 + P⊥ P⊥ → M2 + const = P+ P− = KH (4) where we absorb the constant into M2 . For simplicity, the transverse functions for both the electron and the photon were taken as eigenmodes of the external trap in our initial application (7) which we discuss here (below, we present results with the external trap removed).

The light-front Hamiltonian quantized within a basis function approach as described here offers a promising avenue that capitalizes on theoretical and computational achievements in quantum many-body theory over the past decade. By way of background, one notes that Hamiltonian light-front field theory in a discretized momentum basis (1) and in transverse lattice approaches (2; 3) have shown significant promise. I outline here a Hamiltonian basis function approach following Refs. (4–10) that exploits recent advances in solving the non-relativistic strongly interacting nuclear many-body problem (11; 12).

1997). Effective interactions for mesons and baryons in nuclei, Progr. Theor. , 98, 927-941. V. (2004). Clothed particle representation in quantum field theory: Mass renormalization, Phys. Rev. D 70, 085011. V. (2007). Relativistic interactions for the meson-two-nucleon system in the clothed-particle unitary representation, Ann. , 322, 736-768. ; Glöckle, W. (1999). Approach towards N-nucleon effective generators of the Poincaré group derived from a field theory, Phys. Rev. C 59, 31919-1929. V. (1993).

Download PDF sample

Path integrals, hyperbolic spaces, and Selberg trace formulae by Christian Grosche

by Kevin

Rated 4.22 of 5 – based on 24 votes