Free and Interacting Quantum Fields

The following sections are included:

• Dedication
• Preface
• Introduction
• Contents

The historical evolution of the natural sciences, in general, and of the physics, in particular, took place over a considerable time interval – more than two millennia – culminating in the nowadays understanding of the Universe, essentially based on the concept of the physical field. The bases of the modern field theory were established during the last century, with its newest version – the quantum field theory. This theory met an extraordinary rate of development, many of its aspects being intensively studied even at present time [52, 59, 85, 90, 122, 172, 190, 232, 254, 257, 297, 342, 347, 351, 394, 406, 411]…

The purpose of this chapter is to make a survey on the main aspects connected to the quantum study of the particle interaction in the gravitational field, with astrophysical applications, according to the scientific literature on the subject. The problem of gravitational radiation is also approached…

The following sections are included:

• Tomonaga–Schwinger representation of dynamics of a quantum physical system
• The S-matrix. Matrix elements of the field operators and the Feynman–Dyson-type rules for high-spin particles

The elaboration of the gauge theories played an essential role in conceiving and development of the Standard Model; at present, out of this concept, the unification of the fundamental forces is an impossible action. This way, to thoroughly study all the aspects connected to the gauge fields and their properties became more than necessary, as a condition of a correct comprehension of the theory. This fact is proved by the continuous increase of the number of scientific papers and publications in the above mentioned field of investigation [50, 85, 150, 204, 214, 350]. The special impetus taken by the High Energy Physics (HEP) as a result of the epochal discoveries produced at CERN, Geneva, as well as in some other experimental physics centres provided with particle accelerators, located in USA and Germany, led to an intensification of efforts to comprehend the Microcosmos phenomena from the theoretical physics point of view [16, 47, 170, 191, 200, 221, 261, 303, 355, 410]. On the other side, this impetus represented a premise for enlarging the research area in the domain of gauge theories, in the sense of discovering some new symmetries and/or supersymmetries capable to include in a unitary scheme the multitude of recently discovered particles, and to explain the nature and role of the matter known as dark matter and dark energy…

This chapter is dedicated to the study of interaction of the gravitational field with the matter, by matter being understood the scalar, vectorial and spinorial fields. The interaction Lagrangians were obtained in the frame of the formalism offered by the minimal coupling principle applied in quantum gravity. Using the S-matrix formalism, a general treatment of the first and second-order processes is approached, being obtained – within approximation of external electromagnetic and gravitational fields – several Feynman-type rules for diagrams in the momentum space. Some of the exposed subjects are intended to generalize the results already known in the specific literature…

The following sections are included:

• Gravitational scattering of spin 0, 1/2, 1, 3/2, and 2 massive particles in the centrally-symmetric gravitational field described by the Schwarzschild metric
• Gravitational scattering of spin 0, 1/2, 1, 3/2, and 2 massless particles in the centrally-symmetric gravitational field described by the Schwarzschild metric

The following sections are included:

• General considerations
• Notations and writing conventions
• Electron scattering in external static electromagnetic fields
• Graviton photogeneration in external static electromagnetic fields
• Observations. Some astrophysical applications

The following sections are included:

• Gravitational scattering of spin-0, 1/2, 1, 3/2, and 2 massive particles in the axially-symmetric gravitational field described by the Kerr metric
• Gravitational scattering of massless, spin 0, 1/2, 1, 3/2, and 2 particles in an axially-symmetric field described by the Kerr metric

The complexity of calculations implied in the study of interaction processes of high-spin particles led to creation and usage of some special analytical programs necessary to determine the differential and integral scattering cross-sections of these particles for the interaction processes which take place in both electromagnetic and gravitational external fields…

The following sections are included:

• Appendix A. Isotopic Formalism
• Appendix B. The Dirac Matrices and the Dirac Equation
• Appendix C. Operatorial Transformations
• Appendix D. Singular Functions
• Appendix E. Integration Formulas in Momentum Space
• Appendix F. Matrix Elements of the Field Operators and First-Order Vertices for the Gravitational Interactions of Particles
• Appendix G. Expressions of the Coefficients-Functions of the Differential and Integral Scattering Cross-Sections of Particles in the External Axially-Symmetric Gravitational Field Described by the Kerr Metric
• Appendix H. Values of Some Physical Quantities in CGS and Natural (ħ = 1; c = 1) Unit Systems. Equivalence Between Different Units of Measurement

The following sections are included:

• Bibliography
• Author Index
• Subject Index