feynman''s path integral in quantum theory

... arrow incorrectly by propagating/rotating the contribution from each lower arrow along a SINGLE direct worldline, then summing the results from all these direct worldlines, as it did in constructing ... time integral of the quantity ͑KE Ϫ PE͒ along the path of the particle, namely, Figure 1. A single photon exploring alternative paths in two space dimen- sions. The student clicks to c...

Ngày tải lên: 05/06/2014, 10:58

... principle of least action can be understood in terms of the path integral formulation of quantum mechanics and a corresponding principle of stationary phase. 3 Perturbation theory, the scattering ... diagrammatically in figure 8. In this figure, we use the following Feynman rules: 1. Each line is connected to a sink and a source. 2. Each sink or a source is labeled with a spacetime...

Ngày tải lên: 24/04/2014, 17:10

... physical point of view and still mathematically interesting since, in particular, they display Bose condensation in infinite time. These are the equations describing boson-fermion interactions ... Bose-Einstein entropy) since it would not have physical meaning. In Section 5 we discuss the entropy problem for a gas constituted of electrons and photons. 2.1 Relativistic non quantum gas...

Ngày tải lên: 24/04/2014, 17:14

... no continuous trajectories on a lattice and, hence, no true path integrals in this case. But since in quantum mechanics as well as in quantum field theory the precise definition of a path integral is ... concept of the path integral which is intensively used nowadays in almost all the branches of theoretical physics. The notion of path integral (sometimes also called...

Ngày tải lên: 17/03/2014, 14:31

... still present in the two-dimensional theory, and the theory is in a certain sense maximal quantum: from (33) it is seen that each equivalence class of metrics is included in the path integral with ... problem of defining genuine reparameterization in- variant observables in quantum gravity is present in two dimensional quantum gravity as well. Here we will discuss the...

Ngày tải lên: 17/03/2014, 14:39

... ob- tained by setting ξ = cosh α and η = cos β so that in terms of Cartesian coordinates x = d 2 sinh α sin β cos ϕ, y = d 2 sinh α sin β sin ϕ, z = d 2 cosh α cos β. The range of coordinates ... 30) and  d 2  2  sinh 2 α + sin 2 β  ψ = 1 sinh α ∂ ∂α  sinh α ∂ψ ∂α  + 1 sin β ∂ ∂β  sin β ∂ψ ∂β  +  1 sinh 2 α + 1 sin 2 β  ∂ 2 ψ ∂φ 2 , (1. 31)  d 2  ∇ψ = 1  sinh 2 α + sin 2 β  −...

Ngày tải lên: 17/03/2014, 14:41

Ngày tải lên: 17/03/2014, 14:44

... introductory chapter. In order to get a feeling for adiabatic problems in quantum mechanics and for the concepts involved in their solution, we recall in Section 1.1 the “adiabatic theorem of quantum mechanics” ... sharing their insights on adiabatic problems with me and for their interest in and sup- port of my work. Important parts of the research contained in Chapter 3 and...

Ngày tải lên: 24/04/2014, 17:12

... characterized by the same quantum numbers such as mass, charge and spin, are in principle indistinguishable. From the indistinguishability of particles follows that if two coordinates in an N- particle ... the quantum label ν can contain both discrete and continuous quantum numbers. In that case the symbol  ν is to be interpreted as a combination of both summations and integratio...

Ngày tải lên: 24/04/2014, 17:13