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Title of Journal: Nuovo Cim B

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Abbravation: Il Nuovo Cimento B (1971-1996)

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Società Italiana di Fisica

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DOI

10.1007/978-94-011-2504-8

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1826-9877

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On the theory of identical particles

Authors: J M Leinaas J Myrheim
Publish Date: 2007/10/23
Volume: 37, Issue: 1, Pages: 1-23
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Abstract

The classical configuration space of a system of identical particles is examined Due to the identification of points which are related by permutations of particle indices it is essentially different globally from the Cartesian product of the oneparticle spaces This fact is explicity taken into account in a quantization of the theory As a consequence no symmetry constraints on the wave functions and the observables need to be postulated The two possibilities corresponding to symmetric and antisymmetric wave functions appear in a natural way in the formalism But this is only the case in which the particles move in three or higherdimensional space In one and two dimensions a continuum of possible intermediate cases connects the boson and fermion cases The effect of particle spin in the present formalism is discussedИсследуется классическое конфигурационное пространство системы тождественных частиц Вследствие идентификации точек которые связаны изза перестановок индексов частиц рассматриваемое пространство в целом существенно отличается от декартова произведения одночастичных пространств Этот факт учитывается в явном виде при квантовании теории Как следствие этого необходимо постулировать отсутствие ограничений симметрии на волновые функции и наблюдаемые величины В рассматриваемом формализме естественным образом появляются две возможности сооветствующие симметричной и антисимметричной волновым функциям Указанная ситуация возикает только в случае когда частицы движутся в пространстве трех или большего числа измерений В случае одного и двух измерений континуум возможных промежуточных состояний включает бозонный и фермионный случаи Обсуждается эффект спина частиц в предложенном формализмеSi esamina lo spazio delle configurazioni classico di un sistema di particelle identiche A causa dellidentificazione di punti che sono correlati da permutazioni degli indici delle particelle questo spazio è in modo globale sostanzialmente diverso dal prodotto cartesiano degli spazi ad una particella Si prende in considerazione questo fatto esplicitamente in una quantizzazione della teoria Di conseguenza non è necessario postulare alcuna costrizione di simmetria per le funzioni donda e gli osservabili Le due possibilità corrispondenti a funzioni donda simmetriche e antisimmetriche compaiono nel formalismo in modo naturale Ma questo avviene solo quando le particelle si muovono in uno spazio a 3 o più dimensioni In una o due dimensioni un continuo di possibili casi intermedi collega i casi bosonici e fermionici Si discute leffetto dello spin delle particelle nel presente formalismo


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Other Papers In This Journal:

  1. The algebra of bounded additive operators on a complex Hilbert space
  2. N = 1,2 supergravities in 2 + 1 dimensions as Chern-Simons theories
  3. Maximal acceleration and the time-energy uncertainty relation
  4. Superselection rules; old and new
  5. On the relation between energy and momentum for electrons of a few MeV
  6. Measurements of low-frequency 1/ f α noise in semiconductor polycrystalline thin films of PbTe
  7. Nonrelativistic limit in the algebraic approach of relativistic quantum mechanics
  8. Machian solution with matter injection in cosmology
  9. A note on a quantum-mechanical harmonic oscillator in a space of constant curvature
  10. The gyrofrequency of a charged particle in a constant electromagnetic field. II.—The general result
  11. Magnetic bloch functions
  12. Electromagnetic potential vectors and spontaneous symmetry breaking
  13. Triplet correlations in model liquids
  14. Gravitational-wave tail in Einstein’s linear theory
  15. On the hypothesis that quantum mechanics has a nonlocal structure
  16. A deterministic representation of plane-wave interference
  17. The reconstruction theorem with external sources
  18. Nonabsorption resonances by nonlinear coherent effects in a three-level system
  19. Solution with third-order accuracy for the electron distribution function in weakly ionized gases and intrinsic semiconductors
  20. Probable observation of «excitonic» superconductivity in formvar-aluminum sandwiches
  21. Existence and stability criteria for circular geodesics in the vicinity of a Reissner-Nordström black hole
  22. High-resolution spectroscopy in the far ultraviolet
  23. A theoretical analysis on vibrational-energy transfers in gases
  24. A new calculation of atmospheric neutrino flux
  25. Four-dimensional symmetry from a broad viewpoint
  26. Four-dimensional symmetry from a broad viewpoint
  27. Inhomogeneous positron trapping in fatigued aluminum single crystals
  28. Rotationally symmetric clusters with zero net angular momentum
  29. On exact canonical momenta of collective motion in a many-boson system
  30. Instanton- and monopole-induced compactification of CP N space and chiral fermions in the Einstein-Yang-Mills theory
  31. Variational methods for bound-state problems
  32. Ray propagation in an inviscid fluid
  33. New methods for treatment of spheroidal functions in the solution of scalar wave equation
  34. Dynamics in the Gödel universe
  35. Cauchy initial-value problem and application to Schwarzschild and Friedmann metrics
  36. One-dimensional KDP model with random impurities
  37. Ion-atom cross-sections for sputtering of inert-gas ion incident at low energy on polycrystalline copper target
  38. Conformal conservation laws for second-order scalar fields
  39. Exact solutions of nonlinear differential equations using continued fractions
  40. The classification of spherically symmetric space-times
  41. Radiating collapse of a heat-conducting-fluid sphere with conformally flat interior
  42. Pais-uhlenbeck regularization of free quantum gravity: toward a unitary theory
  43. Local Poincaré generators in the R + T 2 + R 2 theory of Gravity
  44. Beyond the single universe
  45. Transformation de Fourier sur le groupe conforme
  46. Guided optics in rotating dielectric media
  47. Estimation of the contribution of alpha-induced nuclear reactions to the galactic abundances of lithium, beryllium and boron
  48. Limitations and validity of the Hartree-Fock method
  49. Free-electron laser supermodes for bunches with longitudinal energy-position correlation
  50. Classical geometrodynamics revisited
  51. Some cosmological models with constant deceleration parameter
  52. Quantum of London and spin-(l/2)
  53. The Spin-1÷2 Heisenberg ferromagnet via anticommutator Green’s functions utilizing Tyablikov decoupling
  54. Stochastic kinetic theory of strong wave-plasma interaction
  55. Polarization effects in cosmological models with anisotropic curvature
  56. Thermal-ghost fields and unstable systems
  57. Comments on the string theory

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