Quantization of Second-Class Constrained Systems| Quantization of Second-Class Constrained Systems |
In General
> s.a. BRST quantization; types of constrained systems.
* Dirac prescription: To quantize, impose the constraints strongly.
@ References: Grundling & Hurst CMP(88);
Egoryan & Manvelyan TMP(93);
Nakamura & Minowa JMP(93);
Klauder & Shabanov NPB(98)ht/97;
Bratchikov LMP(02) [quantization of Dirac brackets];
Nuramatov & Prokhorov IJGMP(06)qp/05 [reduction to first-class];
Stoilov a1304 [Hilbert-space dimension].
Specific Types of Systems > s.a. Rotor.
@ Particle on a sphere: Kleinert & Shabanov PLA(97);
Hong et al MPLA(00).
@ Motion on general submanifolds: Golovnev IJGMP(06)qp/05 [Dirac prescription];
Golovnev RPMP(09)-a0812-conf [canonical quantization];
Liu JMP(13)-a1305 [particle constrained on a curved hypersurface];
de Oliveira JMP(14)-a1310 [particle constrained on a compact surface];
Xun & Liu AP(14) [Dirac quantization].
@ Time-dependent: Gadjiev & Jafarov JPA(07)ht/06.
Approaches
@ Covariant: Lyakhovich & Marnelius IJMPA(01)ht.
@ BRST approach:
Batalin & Fradkin NPB(87);
Niemi PLB(88);
Batalin et al TMP(01)ht,
PLB(02)ht/01 [generalized, first + second-class].
@ Path-integral approach:
Senjanović AP(76);
Batalin & Marnelius MPLA(01)ht [Lagrangian, as gauge theory];
Chesterman ht/02.
@ Hamilton-Jacobi approach:
Hong et al qp/01.
@ Faddeev-Jackiw approach:
Barcelos-Neto & Wotzasek IJMPA(92).
@ Geometric quantization:
Batalin & Lavrov TMP(16)-a1505.
@ Deformation quantization: Batalin et al JMP(05)ht [general method].
@ Other approaches: Amorim & Thibes JMP(99)ht [BFFT aproach];
Nakamura a1108
[star-product quantization, projection-operator method].
main page
– abbreviations
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