By Ashok Das
This booklet comprises the lectures for a two-semester direction on quantum box idea, and as such is gifted in a rather casual and private demeanour. The direction starts off with relativistic one-particle structures, and develops the fundamentals of quantum box idea with an research of the representations of the Poincaré staff. Canonical quantization is conducted for scalar, fermion, Abelian and non-Abelian gauge theories. Covariant quantization of gauge theories can be performed with a close description of the BRST symmetry. The Higgs phenomenon and the normal version of electroweak interactions also are constructed systematically. Regularization and (BPHZ) renormalization of box theories in addition to gauge theories are mentioned intimately, resulting in a derivation of the renormalization workforce equation. furthermore, chapters -- one at the Dirac quantization of limited structures and one other on discrete symmetries -- are integrated for completeness, even though those should not lined within the two-semester direction
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6) p1 = p2 = 0. 7) Let us simplify the calculation by restricting to motion along the z-axis. In other words, let us set In this case, the equation takes the form (γ 0 p0 + γ 3 p3 − m)u(p) = 0. 1 Plane wave solutions 29 This is a set of four linear homogeneous equations and a nontrivial solution exists only if the determinant of the coefficient matrix vanishes. 10) we obtain, (p0 − m) (p0 − m)(p0 + m)2 − p23 (p0 + m) +p3 p33 + (p0 − m)(−p3 (p0 + m)) = 0, or, or, or, (p20 − m2 )2 − 2p23 (p20 − m2 ) + p43 = 0, (p20 − p23 − m2 )2 = 0, p20 − p23 − m2 = 0.
3) defines a set of matrix equations. Since the Dirac matrices, γ µ , are 4 × 4 matrices, the wave functions, in this case, are four component column matrices (column vectors). From the study of angular momentum, we know that multicomponent wave functions suggest a nontrivial spin angular momentum. ) Therefore, we expect the solutions of the Dirac equation to describe particles with spin. To understand what kind of particles are described by the Dirac equation, let us look at the plane wave solutions of the equation (which are supposed to describe free particles).
A. Das, Lectures on Quantum Mechanics, Hindustan Publishing, New Delhi, India, 2003. 3) defines a set of matrix equations. Since the Dirac matrices, γ µ , are 4 × 4 matrices, the wave functions, in this case, are four component column matrices (column vectors). From the study of angular momentum, we know that multicomponent wave functions suggest a nontrivial spin angular momentum. ) Therefore, we expect the solutions of the Dirac equation to describe particles with spin. To understand what kind of particles are described by the Dirac equation, let us look at the plane wave solutions of the equation (which are supposed to describe free particles).
Lectures on Quantum Field Theory by Ashok Das