SCALAR FIELD THEORY ON A KÄHLER MANIFOLD

1989 ◽  
Vol 04 (12) ◽  
pp. 1127-1134
Author(s):  
K.M. COSTA
Keyword(s):  
Scalar Field ◽  
Kernel Methods ◽  
Background Field ◽  
Field Theories ◽  
Coset Space ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Polynomial Complex ◽  
Loop Counter ◽  
Kählerian Manifold

The invariant one-loop counter terms for a class of non-polynomial complex scalar field theories are found using the background field geodesic expansion together with heat kernel methods. These theories have dynamics invariant under a group G with fields that transform linearly only under a subgroup H of G. The fields are coordinates on a complex Kählerian manifold corresponding to the coset space G/H. The technique is applied to the CP n model.

FIELD REDEFINITION AND RENORMALIZABILITY IN SCALAR FIELD THEORIES

2013 ◽  
Vol 28 (25) ◽  
pp. 1350123
Author(s):  
N. MOHAMMEDI
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Background Field ◽  
Polar Coordinates ◽  
Complex Scalar ◽  
Change Of Variables ◽  
Single Complex ◽  
Complex Scalar Field ◽  
Field Redefinition

We have addressed the issue of field redefinition in connection with renormalizability. Our study is restricted to theories of interacting scalar fields. We have, in particular, shown that if a theory is renormalizable in the usual power-counting sense then it remains renormalizable in the same sense after a change of variables. This is due to the use of the powerful method of the background field expansion. In the case of a single complex scalar field, it turns out that the determination of the counterterms is much simpler when polar coordinates are used. We illustrate this by carrying out a one-loop calculation in the latter case.

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.

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