Search results for "First quantization"
showing 3 items of 3 documents
Quantum Mechanics of Point Particles
2013
In developing quantum mechanics of pointlike particles one is faced with a curious, almost paradoxical situation: One seeks a more general theory which takes proper account of Planck’s quantum of action \(h\) and which encompasses classical mechanics, in the limit \(h\rightarrow 0\), but for which initially one has no more than the formal framework of canonical mechanics. This is to say, slightly exaggerating, that one tries to guess a theory for the hydrogen atom and for scattering of electrons by extrapolation from the laws of celestial mechanics. That this adventure eventually is successful rests on both phenomenological and on theoretical grounds.
Supersymmetric particle model with additional bosonic coordinates
1986
A new supersymmetric particle model in enlarged superspace with additional bosonic coordinateszij,\(\bar z_{ij} \) (zij=−zji;i=1...N, N even) canonically conjugated to central charges is quantized. The superwave functions which are obtained through first quantization are the free superfields on the enlarged superspace\((x^\mu , \theta _{\alpha i} , \bar \theta _i^{\dot \alpha } , z_{ij} , \bar z_{ij} )\). Two particular cases (N=2 with one additional complex bosonic coordinate andN=8 with seven additional real coordinates) are considered in more detail.
Two-twistor particle models and free massive higher spin fields
2015
We present D=3 and D=4 models for massive particles moving in a new type of enlarged spacetime, with D-1 additional vector coordinates, which after quantization lead to the towers of massive higher spin (HS) free fields. Two classically equivalent formulations are presented: one with a hybrid spacetime/bispinor geometry and a second described by a free two-twistor dynamics with constraints. After quantization in the D=3 and D=4 cases, the wave functions are given as functions on the SL(2,R) and SL(2,C) group manifolds respectively, and describe arbitrary on-shell momenta and spin degrees of freedom. Finally, the D=6 case and possible supersymmetric extensions are mentioned.