By Hagen Kleinert
This is the 5th, increased version of the excellent textbook released in 1990 at the idea and functions of direction integrals. it's the first booklet to explicitly resolve direction integrals of a large choice of nontrivial quantum-mechanical platforms, specifically the hydrogen atom. The options were made attainable through significant advances. the 1st is a new euclidean course fundamental formula which raises the limited variety of applicability of Feynman's time-sliced formulation to incorporate singular appealing 1/r- and 1/r2-potentials. the second one is a new nonholonomic mapping principle sporting actual legislation in flat spacetime to spacetimes with curvature and torsion, which results in time-sliced course integrals which are obviously invariant lower than coordinate transformations.
In addition to the time-sliced definition, the writer provides a perturbative, coordinate-independent definition of direction integrals, which makes them invariant below coordinate modifications. A constant implementation of this estate ends up in an extension of the idea of generalized features through defining uniquely items of distributions.
The robust Feynman-Kleinert variational technique is defined and built systematically right into a variational perturbation theory which, not like traditional perturbation conception, produces convergent effects. The convergence is uniform from vulnerable to powerful couplings, beginning how to distinct reviews of analytically unsolvable direction integrals within the strong-coupling regime the place they describe severe phenomena.
Tunneling procedures are handled intimately, with purposes to the lifetimes of supercurrents, the steadiness of metastable thermodynamic stages, and the large-order habit of perturbation expansions. A variational therapy extends the variety of validity to small limitations. A corresponding extension of the large-order perturbation thought now additionally applies to small orders.
Special consciousness is dedicated to course integrals with topological regulations had to comprehend the statistical houses of hassle-free debris and the entanglement phenomena in polymer physics and biophysics. The Chern–Simons idea of debris with fractional information (anyons) is brought and utilized to give an explanation for the fractional quantum corridor effect.
The relevance of direction integrals to monetary markets is mentioned, and enhancements of the well-known Black–Scholes formulation for choice costs are constructed which account for the actual fact, lately skilled on this planet markets, that giant fluctuations ensue even more often than in Gaussian distributions.
- Path Integrals — basic houses and straightforward Solutions
- External assets, Correlations, and Perturbation Theory
- Semiclassical Time Evolution Amplitude
- Variational Perturbation Theory
- Path Integrals with Topological Constraints
- Many Particle Orbits — facts and moment Quantization
- Path Integrals in Polar and round Coordinates
- Wave Functions
- Spaces with Curvature and Torsion
- Schrödinger Equation often Metric-Affine Spaces
- New direction indispensable formulation for Singular Potentials
- Path fundamental of Coulomb System
- Solution of additional direction Integrals through Duru-Kleinert Method
- Path Integrals in Polymer Physics
- Polymers and Particle Orbits in Multiply hooked up Spaces
- Nonequilibrium Quantum Statistics
- Relativistic Particle Orbits
- Path Integrals and fiscal Markets
Readership: scholars and researchers in theoretical physics.
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