Second Quantization and Lorentz Invariance. II

Journal Article · Tue May 01 04:00:00 EDT 1962 · Progress of Theoretical Physics (Kyoto)

DOI:https://doi.org/10.1143/PTP.27.936· OSTI ID:4759514

Sato, Shigeo

The expansion of the hamiltonian in 1/c², which may be used to get the general form of the covariant Hamiltonian for a system of a fixed number of particles, is applied to a second-quantized system to obtain a convergent and covariant hamiltonian formalism. In this case, it is shown that if the interaction terms are commutable with EPSILON /m _iN_i, where m_i 's and N_i's are masses and number operators of concerned particles, the expansion in 1/c² can be performed. As a result, a possible method to construct a hamiltonian formalism for the second quantized system is obtained. Moreover, if some suitable relation exists between concerned masses, the interchange of particles can be treated to some extent. An example is given to clarify this method. The method can not be applied to the case where a massless particle is involved. A tentative method for such a case is proposed, comprising expansion of the hamiltonian in 1/c. The relation between spin and statistics is discussed.

• Research Organization: Rikkyo Univ., Tokyo
• Sponsoring Organization: USDOE
• NSA Number: NSA-16-032328
• OSTI ID: 4759514
• Journal Information: Progress of Theoretical Physics (Kyoto), Journal Name: Progress of Theoretical Physics (Kyoto) Journal Issue: 5 Vol. 27; ISSN 0033-068X
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
HAMILTONIAN
INTERACTIONS
LORENTZ TRANSFORMATIONS
QUANTUM MECHANICS
RELATIVITY THEORY
SPIN
STATISTICS