scholarly journals The Feynman-Dyson propagators for neutral particles (locality or non-locality?)

2019 ◽  
Vol 65 (6 Nov-Dec) ◽  
pp. 612
Author(s):  
Valeriy V. Dvoeglazov
Keyword(s):  
Clifford Algebra ◽  
Fock Space ◽  
Field Operator ◽  
Neutral Particles ◽  
Charge Conjugate ◽  
Mathematical Foundations ◽  
Conjugate States ◽  
Non Locality

An analog of the $S=1/2$ Feynman-Dyson propagator is presented in the framework of the $S=1$ Weinberg's theory.The basis for this construction is the concept of the Weinberg field as a system of four field functions differing by parity and by dual transformations.Next, we analyze the recent controversy in the definitions of the Feynman-Dyson propagator for the field operator containing the $S=1/2$ self/anti-self charge conjugate states in the papers by D. Ahluwalia et al. and by W. Rodrigues Jr. et al. The solution of this mathematical controversy is obvious. It is related to the necessary doubling of the Fock Space (as in the Barut and Ziino works), thus extending the corresponding Clifford Algebra. However, the logical interrelations of different mathematical foundations with the physical interpretations are not so obvious. Physics should choose only one correct formalism- it is not clear, why two correct mathematical formalisms (which are based on the same postulates) lead to different physical results?

ENTANGLED EIGENSTATES AND SQUEEZING OPERATOR FOR COMPLEX SCALAR FIELDS

1999 ◽  
Vol 14 (39) ◽  
pp. 2695-2700 ◽  
Author(s):  
HONG-YI FAN ◽  
ZENG-BING CHEN
Keyword(s):  
Quantum Mechanics ◽  
Fock Space ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Charge Conjugate ◽  
Einstein Podolsky Rosen ◽  
Squeezing Operator

We derive the entangled eigenstate ‖ξ> of complex scalar fields ϕ and ϕ† in the Fock space. The ‖ξ> state is found to embed the entanglement possessed by the Einstein–Podolsky–Rosen states in quantum mechanics. The ‖ξ> set spans a complete and orthonormal representation. The advantage of the new <ξ‖-representation helps us to derive the normally ordered forms of the squeezing and charge conjugate operators for complex scalar fields rather easily.

QUANTUM STOCHASTIC CALCULUS ON BOOLEAN FOCK SPACE

2004 ◽  
Vol 07 (04) ◽  
pp. 631-650 ◽  
Author(s):  
ANIS BEN GHORBAL ◽  
MICHAEL SCHÜRMANN
Keyword(s):  
Fock Space ◽  
Field Operator ◽  
Stochastic Calculus ◽  
Product Formula ◽  
Stochastic Integration ◽  
Quantum Stochastic Calculus ◽  
Basic Field ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups

In this paper we establish a theory of stochastic integration with respect to the basic field operator processes in the Boolean case. This leads to a Boolean version of quantum Itô's product formula and has applications to the theory of dilations of quantum dynamical semigroups.

Interacting Fock Spaces Related to the Anderson Model

1998 ◽  
Vol 01 (02) ◽  
pp. 247-283 ◽  
Author(s):  
Yun-Gang Lu
Keyword(s):  
Integral Equation ◽  
Distribution Function ◽  
Anderson Model ◽  
Fock Space ◽  
Field Operator ◽  
Vacuum Expectation ◽  
Fock Spaces ◽  
Test Functions ◽  
Test Function ◽  
New Type

A new type of interacting Boltzmannian Fock space, emerging from the stochastic limit of the Anderson model, is investigated. We describe the structure of the space and the form, assumed in this case, by the principles of factorization and of total connection. Using these principles, the vacuum expectation of any product of creation and annihilation operators can be calculated. By means of these results, for any test function, a system of diffrence equations satisfied by the moments of the field operator and an integral equation satisfied by their generating function is deduced. In many interesting cases this equation is solved and the vacuum distribution function of the field operator (even its density) is explicitly determined. This evidentiates a new phenomenon which cannot take place in the usual Fock spaces (and did not appear in the simplest examples of interacting Fock spaces): by taking different test functions, the vacuum distribution of the field operator does not change only parametrically, but radically. In particular we find the semi-circle, the reciprocal-semi-circle (or Arcsine), the double-beta,…, and many other distributions.

scholarly journals Interacting Fock Spaces and Gaussianization of Probability Measures

1998 ◽  
Vol 01 (04) ◽  
pp. 663-670 ◽  
Author(s):  
Luigi Accardi ◽  
Marek Bożejko
Keyword(s):  
Probability Measure ◽  
Orthogonal Polynomials ◽  
Fock Space ◽  
Field Operator ◽  
Multiplication Operator ◽  
Probability Measures ◽  
Number Operator ◽  
Infinitely Divisible ◽  
Future Paper ◽  
Interacting Fock Space

We prove that any probability measure on ℝ, with moments of all orders, is the vacuum distribution, in an appropriate interacting Fock space, of the field operator plus (in the nonsymmetric case) a function of the number operator. This follows from a canonical isomorphism between the L2-space of the measure and the interacting Fock space in which the number vectors go into the orthogonal polynomials of the measure and the modified field operator into the multiplication operator by the x-coordinate. A corollary of this is that all the momenta of such a measure are expressible in terms of the Szëgo–Jacobi parameters, associated to its orthogonal polynomials, by means of diagrams involving only noncrossing pair partitions (and singletons, in the nonsymmetric case). This means that, with our construction, the combinatorics of the momenta of any probability measure (with all moments) is reduced to that of a generalized Gaussian. This phenomenon we call Gaussianization. Finally we define, in terms of the Szëgo–Jacobi parameters, a new convolution among probability measures which we call universal because any probability measure (with all moments) is infinitely divisible with respect to this convolution. All these results will be extended to the case of many (in fact infinitely many) variables in a future paper.

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