Axioms of Relativistic Quantum Field Theory
... 70 years a generally accepted and rigorous description of the structure of quantum field theories does not exist. In many instances quantum field theory is approached by quantizing classical field theories as for example elaborated in the last chapter on strings. A more systematic specification uses ...
... 70 years a generally accepted and rigorous description of the structure of quantum field theories does not exist. In many instances quantum field theory is approached by quantizing classical field theories as for example elaborated in the last chapter on strings. A more systematic specification uses ...
preskill-ARO-2013 - Caltech Particle Theory
... given site). We could represent fermion operators as (Jordan-Wigner) nonlocal string operators at cost O(L), or we could store the partial sums of mode ...
... given site). We could represent fermion operators as (Jordan-Wigner) nonlocal string operators at cost O(L), or we could store the partial sums of mode ...
Lecture 22 Relativistic Quantum Mechanics
... mass energy, p ∼ mc particles enter regime where relativity intrudes on quantum mechanics. At these energy scales qualitatively new phenomena emerge: e.g. particle production, existence of antiparticles, etc. By applying canonical quantization procedure to energy-momentum invariant, we are led to th ...
... mass energy, p ∼ mc particles enter regime where relativity intrudes on quantum mechanics. At these energy scales qualitatively new phenomena emerge: e.g. particle production, existence of antiparticles, etc. By applying canonical quantization procedure to energy-momentum invariant, we are led to th ...
Electrodynamic Containment of Charged Particles
... development of a method of containing these particles in dynamic equilibrium by alternating electric fields. 1 ,2 This new technique is based upon the strong focusing principle which has as its analogue the classical problem of the upside-down pendulum. Essentially this device can be thought of as a ...
... development of a method of containing these particles in dynamic equilibrium by alternating electric fields. 1 ,2 This new technique is based upon the strong focusing principle which has as its analogue the classical problem of the upside-down pendulum. Essentially this device can be thought of as a ...
Second Quantization
... This describes particles moving in a background potential U (r), and interacting via a potential V (r). In the last sum, i and j range from 1 to N , but terms where i = j are excluded as they are self-interactions that we don’t want to consider (even if we do include them, they just give a constant ...
... This describes particles moving in a background potential U (r), and interacting via a potential V (r). In the last sum, i and j range from 1 to N , but terms where i = j are excluded as they are self-interactions that we don’t want to consider (even if we do include them, they just give a constant ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.