A functional integral algorithm for the partition function and for the temperature Green’s function generating functional of spin 1/2 systems is developed. Starting from the representation of the spin operators in terms of fermion creation and destruction operators we write the above mentioned objects as functional integrals over an infinite dimensional Grassmann algebra. We show how to eliminate the integration over the Grassmann algebra in favor of an integration over function space. The use of the formalism is illustrated with two simple examples.A functional integral algorithm for the partition function and for the temperature Green’s function generating functional of spin 1/2 systems is developed. Starting from the representation of the spin operators in terms of fermion creation and destruction operators we write the above mentioned objects as functional integrals over an infinite dimensional Grassmann algebra. We show how to eliminate the integration over the Grassmann algebra in favor of an integration over function space. The use of the formalism is illustrated with two simple examples.

Journal of Mathematical PhysicsJun 1, 19802 citations

Generalized Fock spaces, new forms of quantum statistics and their algebras

A.K. Mishra, G. Rajasekaran, Taramani Madras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as "infinite", Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are : new algebras for infinite statistics, q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, "doubly-infinite" statistics, many representations of orthostatistics, Hubbard statistics and its variations. Key Words : Fock space -- multioscillator algebras -- q-deformation -- quantum groups -- general...We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as "infinite", Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are : new algebras for infinite statistics, q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, "doubly-infinite" statistics, many representations of orthostatistics, Hubbard statistics and its variations. Key Words : Fock space -- multioscillator algebras -- q-deformation -- quantum groups -- general...

Jan 1, 199414 citations

Operator Algebras and Identities

V. Balakrishnan

Springer eBooksJan 1, 20200 citations

Creation and Annihilation Operators

Springer eBooksSep 2, 20083 citations

Solution of a Multiatom Radiation Model Using the Bargmann Realization of the Radiation Field

William R. Mallory

A model for interacting single-mode electromagnetic radiation and matter consisting of $N$ two-level particles is solved exactly using a representation in which the creation and destruction operators for the field act by multiplication and differentiation, respectively. The model includes off-resonant interactions. Closed-form expressions can be given for some special cases. The solutions are transformed to the more familiar Fock and Schr\"odinger representations. Numerical results are given to indicate the behavior of the solutions. An equation for a generating function is derived which would give solutions of the (algebraic) matrix equation to which the problem has been reduced.A model for interacting single-mode electromagnetic radiation and matter consisting of $N$ two-level particles is solved exactly using a representation in which the creation and destruction operators for the field act by multiplication and differentiation, respectively. The model includes off-resonant interactions. Closed-form expressions can be given for some special cases. The solutions are transformed to the more familiar Fock and Schr\"odinger representations. Numerical results are given to indicate the behavior of the solutions. An equation for a generating function is derived which would give solutions of the (algebraic) matrix equation to which the problem has been reduced.

Physical ReviewDec 25, 196944 citations

A model for interacting single-mode electromagnetic radiation and matter consisting of

N

two-level particles is solved exactly using a representation in which the creation and destruction operators for the field act by multiplication and differentiation, respectively. The model includes off-resonant interactions. Closed-form expressions can be given for some special cases. The solutions are transformed to the more familiar Fock and Schr\"odinger representations. Numerical results are given to indicate the behavior of the solutions. An equation for a generating function is derived which would give solutions of the (algebraic) matrix equation to which the problem has been reduced.