Quantum field theory for elementary particles. Is quantum field theory a theory?

Quantum Field Theory for Elementary Particles

Elementary Particles in a Quantum Theory over a Galois Field

We consider elementary particles in a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily describes a particle and its antiparticle simultaneously. In other words, the very existence of antiparticles is a strong indication that nature is described...

What Is a Quantum Field Theory ?

Introduction. Quantum field theory began in 1927 with a paper by Dirac [1] in which he sought a framework that would unite the classical electromagnetism of Maxwell with quantum mechanics. Ever since then it has been under continuous scrutiny by physicists, which illustrates the fact that in some ways, physics is more highly focused than mathematics. A mathematician is not forced to work on the...

Quantum Field Theory Course

Part I. Classical Mechanics 9 0. Intro 9 0.1. Mechanical systems 9 0.2. Lagrangian and Hamiltonian formulation 9 1. Lagrangian approach 10 1.1. Manifolds 10 1.2. Differentiation 11 1.3. Calculus of Variations on an interval 11 1.4. Lagrangian reformulation of Newton‘s equation 13 2. Hamiltonian approach 14 2.1. Metrics: linear algebra 14 2.2. The passage to the cotangent vector bundle via the k...

Quantum field theory

The author discusses the general principles underlying quantum field theory and attempts to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. A few of quantum field theory’s most striking successes, both achieved and prospective are mentioned, and possible limitations of the theory are ...