scholarly journals Some exact solutions of reduced scalar Yukawa theory

1998 ◽  
Vol 76 (7) ◽  
pp. 523-537 ◽  
Author(s):  
J W Darewych
Keyword(s):  
Scalar Field ◽  
Vacuum State ◽  
Analytic Solutions ◽  
Green Functions ◽  
Yukawa Model ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Three Body ◽  
Yukawa Theory ◽  
Body Case

The scalar Yukawa model, in which a complex scalar field, ϕ, interacts via a real scalar field, χ, is reduced by using covariant Green functions. It is shown that exact few-particle eigenstates of the truncated QFT Hamiltonian can be obtained in the Feshbach–Villars formulation if an unorthodox "empty" vacuum state is used. Analytic solutions for the two-body case are obtained for massless chion exchange in 3+1 dimensions and for massive chion exchange in 1+1 dimensions. Comparison is made to ladder Bethe–Salpeter, Feynman–Schwinger, and quasipotential results for massive chion exchange in 3+1. Equations for the three-body case are also obtained. PACS Nos.: 11.10.Ef, 11.10.Qr, and 03.70.+k

scholarly journals ON THE RESPONSE OF DETECTORS IN CLASSICAL ELECTROMAGNETIC BACKGROUNDS

1999 ◽  
Vol 14 (27) ◽  
pp. 1869-1877 ◽  
Author(s):  
L. SRIRAMKUMAR
Keyword(s):  
Scalar Field ◽  
Vacuum State ◽  
Quantum Field ◽  
Inertial Motion ◽  
Complex Scalar ◽  
Different Types ◽  
Complex Scalar Field ◽  
Number Of Particles

We study the response of a detector that is coupled nonlinearly to a quantized complex scalar field in different types of classical electromagnetic backgrounds. Assuming that the quantum field is in the vacuum state, we show that, when in inertial motion, the detector responds only when the electromagnetic background produces particles. However, we find that the response of the detector is not proportional to the number of particles produced by the background.

The classical and quantum cosmology with a complex scalar field

1992 ◽  
Vol 169 (4) ◽  
pp. 308-312 ◽  
Author(s):  
I.M. Khalatnikov ◽  
A. Mezhlumian
Keyword(s):  
Scalar Field ◽  
Quantum Cosmology ◽  
Complex Scalar ◽  
Complex Scalar Field

Self-interacting complex scalar field as dark matter

2011 ◽  
Author(s):  
F. Briscese ◽  
Luis Arturo Ureña-López ◽  
Hugo Aurelio Morales-Técotl ◽  
Román Linares-Romero ◽  
Elí Santos-Rodríguez ◽  
...  
Keyword(s):  
Dark Matter ◽  
Scalar Field ◽  
Complex Scalar ◽  
Complex Scalar Field

scholarly journals Hadamard parametrix of the Feynman Green’s function of a five-dimensional charged scalar field

2020 ◽  
Vol 29 (11) ◽  
pp. 2041002
Author(s):  
Visakan Balakumar ◽  
Elizabeth Winstanley
Keyword(s):  
Scalar Field ◽  
Green’S Function ◽  
Green's Function ◽  
Minkowski Spacetime ◽  
Energy Tensor ◽  
Complex Scalar ◽  
Charged Scalar ◽  
Taylor Series Expansions ◽  
Complex Scalar Field ◽  
Charged Scalar Field

The Hadamard parametrix is a representation of the short-distance singularity structure of the Feynman Green’s function for a quantum field on a curved spacetime background. Subtracting these divergent terms regularizes the Feynman Green’s function and enables the computation of renormalized expectation values of observables. We study the Hadamard parametrix for a charged, massive, complex scalar field in five spacetime dimensions. Even in Minkowski spacetime, it is not possible to write the Feynman Green’s function for a charged scalar field exactly in closed form. We, therefore, present covariant Taylor series expansions for the biscalars arising in the Hadamard parametrix. On a general spacetime background, we explicitly state the expansion coefficients up to the order required for the computation of the renormalized scalar field current. These coefficients become increasingly lengthy as the order of the expansion increases, so we give the higher-order terms required for the calculation of the renormalized stress-energy tensor in Minkowski spacetime only.

Field models

2021 ◽  
pp. 42-69
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Spinor Field ◽  
Vector Fields ◽  
Sigma Model ◽  
Complex Scalar ◽  
Yang Mills ◽  
Scalar Field Models ◽  
Complex Scalar Field ◽  
Mills Field

This chapter provides constructions of Lagrangians for various field models and discusses the basic properties of these models. Concrete examples of field models are constructed, including real and complex scalar field models, the sigma model, spinor field models and models of massless and massive free vector fields. In addition, the chapter discusses various interactions between fields, including the interactions of scalars and spinors with the electromagnetic field. A detailed discussion of the Yang-Mills field is given as well.

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