1 Introduction
3
the ultraviolet behavior, also allows to remove the dangerous infrared divergences
arising due to the UV/IR mechanism. Further, the non(anti)commutativity has been
introduced also to the fermionic sector [31], however, actually it implies in modifying
the corresponding superfield action by a small number of additive terms proportional
to lower degrees of the non(anti)commutativity parameter. In all other aspects, there
is no essential difference between superfield theories formulated on the base of
the fermionic noncommutativity and the usual ones, and in these lecture notes, the
fermionic non(anti)commutativity is discussed only very briefly.
The N = 1 superfield methodology in supersymmetric quantum field theory,
being an universal tool for a great number of supersymmetric models, is a main
topic of these lectures. We consider the superfield description both of three- and
four-dimensional supersymmetric field theories, including the noncommutative generalization for some cases. In the chapter devoted to three-dimensional theories we
use the notations and conventions introduced in [23], while in the chapter devoted to
four-dimensional theories—those ones introduced in [32, 33].
Within this review, we are going not only to describe the superfield formalism in
three- and four-dimensional space-times and give the superfield formulation for the
most important examples of the supersymmetric field theories, but also to consider in
details many examples of calculating loop corrections within the superfield description. Our review is focused, principally, in evaluating a superfield effective action in
various supersymmetric field theories. Because of the restricted value of the lecture
course, we do not discuss here the superstring and supergravity issues, for which we
recommend [1, 33] respectively.
The structure of this review looks like follows. In the Chap. 2, we give a basic
description of an effective action and the loop expansion. In the Chap. 3 we discuss
the superfield formalism, the supergraph technique and methods of calculating the
superfield effective action in the three-dimensional space-time. In the Chap. 4, the
four-dimensional superfield methodology is described, and many examples of quantum calculations are given. In the Chap. 5, we present the introduction to the problem
of a supersymmetry breaking. Finally, in the Summary we discuss the perspectives
and applications of supersymmetry.
3
the ultraviolet behavior, also allows to remove the dangerous infrared divergences
arising due to the UV/IR mechanism. Further, the non(anti)commutativity has been
introduced also to the fermionic sector [31], however, actually it implies in modifying
the corresponding superfield action by a small number of additive terms proportional
to lower degrees of the non(anti)commutativity parameter. In all other aspects, there
is no essential difference between superfield theories formulated on the base of
the fermionic noncommutativity and the usual ones, and in these lecture notes, the
fermionic non(anti)commutativity is discussed only very briefly.
The N = 1 superfield methodology in supersymmetric quantum field theory,
being an universal tool for a great number of supersymmetric models, is a main
topic of these lectures. We consider the superfield description both of three- and
four-dimensional supersymmetric field theories, including the noncommutative generalization for some cases. In the chapter devoted to three-dimensional theories we
use the notations and conventions introduced in [23], while in the chapter devoted to
four-dimensional theories—those ones introduced in [32, 33].
Within this review, we are going not only to describe the superfield formalism in
three- and four-dimensional space-times and give the superfield formulation for the
most important examples of the supersymmetric field theories, but also to consider in
details many examples of calculating loop corrections within the superfield description. Our review is focused, principally, in evaluating a superfield effective action in
various supersymmetric field theories. Because of the restricted value of the lecture
course, we do not discuss here the superstring and supergravity issues, for which we
recommend [1, 33] respectively.
The structure of this review looks like follows. In the Chap. 2, we give a basic
description of an effective action and the loop expansion. In the Chap. 3 we discuss
the superfield formalism, the supergraph technique and methods of calculating the
superfield effective action in the three-dimensional space-time. In the Chap. 4, the
four-dimensional superfield methodology is described, and many examples of quantum calculations are given. In the Chap. 5, we present the introduction to the problem
of a supersymmetry breaking. Finally, in the Summary we discuss the perspectives
and applications of supersymmetry.