This is the 5th, multiplied variation of the excellent textbook released in 1990 at the conception and purposes of direction integrals. it's the first e-book to explicitly clear up direction integrals of a large choice of nontrivial quantum-mechanical structures, specifically the hydrogen atom. The strategies were made attainable by way of significant advances. the 1st is a *new euclidean direction essential formula* which raises the constrained diversity of applicability of Feynman's time-sliced formulation to incorporate singular beautiful 1/*r*- and 1/*r*^{2}-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 glaringly invariant less 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 lower than coordinate changes. A constant implementation of this estate results in an extension of the idea of generalized capabilities by way of defining uniquely items of distributions.

The robust Feynman-Kleinert variational method is defined and constructed systematically right into a *variational perturbation theory* which, not like traditional perturbation thought, produces convergent effects. The convergence is uniform from vulnerable to robust couplings, starting how to certain reviews of analytically unsolvable direction integrals within the strong-coupling regime the place they describe serious phenomena.

Tunneling procedures are taken care of intimately, with functions to the lifetimes of supercurrents, the soundness of metastable thermodynamic stages, and the large-order habit of perturbation expansions. A variational remedy extends the variety of validity to small obstacles. A corresponding extension of the large-order perturbation concept now additionally applies to small orders.

Special consciousness is dedicated to direction integrals with topological regulations had to comprehend the statistical homes of basic debris and the entanglement phenomena in polymer physics and biophysics. The Chern–Simons idea of debris with fractional records *(anyons)* is brought and utilized to give an explanation for the fractional quantum corridor effect.

The relevance of course integrals to monetary markets is mentioned, and enhancements of the recognized Black–Scholes formulation for choice costs are constructed which account for the very fact, lately skilled on the planet markets, that giant fluctuations take place even more often than in Gaussian distributions.

**Contents:**

- Fundamentals
- Path Integrals — straightforward houses and easy Solutions
- External resources, Correlations, and Perturbation Theory
- Semiclassical Time Evolution Amplitude
- Variational Perturbation Theory
- Path Integrals with Topological Constraints
- Many Particle Orbits — records and moment Quantization
- Path Integrals in Polar and round Coordinates
- Wave Functions
- Spaces with Curvature and Torsion
- Schrödinger Equation typically Metric-Affine Spaces
- New direction vital formulation for Singular Potentials
- Path critical of Coulomb System
- Solution of extra direction Integrals by means of Duru-Kleinert Method
- Path Integrals in Polymer Physics
- Polymers and Particle Orbits in Multiply hooked up Spaces
- Tunneling
- Nonequilibrium Quantum Statistics
- Relativistic Particle Orbits
- Path Integrals and monetary Markets

**Readership:** scholars and researchers in theoretical physics.