A THEORY OF ALGEBRAIC INTEGRATION

In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such spaces. We consider this problem and we show how to define an integration which respects the physical principle of composition of the probability amplitudes for a very large class of algebras.

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Path-integral approach to the one-dimensional large-UHubbard model

Physical Review B ◽

10.1103/physrevb.45.7850 ◽

1992 ◽

Vol 45 (14) ◽

pp. 7850-7871 ◽

Cited By ~ 34

Author(s):

Z. Y. Weng ◽

D. N. Sheng ◽

C. S. Ting ◽

Z. B. Su

Keyword(s):

Path Integral ◽

Integral Approach ◽

One Dimensional ◽

Path Integral Approach ◽

The One

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Path-integral approach to anomalies at finite temperature

Canadian Journal of Physics ◽

10.1139/p90-015 ◽

1990 ◽

Vol 68 (1) ◽

pp. 96-103 ◽

Cited By ~ 1

Author(s):

T. F. Treml

Keyword(s):

Vector Field ◽

Path Integral ◽

Finite Temperature ◽

Dimensional Regularization ◽

Flat Space ◽

Integral Approach ◽

Chiral Anomaly ◽

Conformal Anomaly ◽

Path Integral Approach ◽

The One

The non-Abelian chiral anomaly for a fermion interacting with an external vector field in any even dimension and the conformal anomaly, in the limit of flat space–time, for a self-interacting scalar field are shown to be independent of temperature using a simple path-integral approach that employs dimensional regularization. The chiral anomaly is used as an example to show that the methods used to study the dimensionally regularized anomaly at finite temperature are readily transferable to the case of ζ-function regularization. The conformal anomaly in (super) string theory at finite temperature is briefly discussed in the light of known results. Some subtleties concerning the use of infrared cutoffs in a dimensionally regularized approach to the computation of the one-loop effective action at finite temperature are considered in an appendix.

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A PATH INTEGRAL APPROACH TO DERIVATIVE SECURITY PRICING I: FORMALISM AND ANALYTICAL RESULTS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024999000200 ◽

1999 ◽

Vol 02 (04) ◽

pp. 381-407 ◽

Cited By ~ 31

Author(s):

ELEONORA BENNATI ◽

MARCO ROSA-CLOT ◽

STEFANO TADDEI

Keyword(s):

Financial Markets ◽

Path Integral ◽

Integral Approach ◽

Covariant Formulation ◽

One Dimensional ◽

Path Integral Approach ◽

Financial Interest ◽

Security Pricing ◽

The One ◽

Pde Methods

We use a path integral approach for solving the stochastic equations underlying the financial markets, and show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the multi-dimensional cases, with point dependent drift and volatility, and describe a covariant formulation which allows general changes of variables. Finally we apply the method to some economic models with analytical solutions. In particular, we evaluate the expectation value of functionals which correspond to quantities of financial interest.

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