First-quantized para-particle theory

Yoshio Ohnuki, S. Kamefuchi

Douglas J. Klein

Abstract First, the spin‐free formulation of electronic structure is reviewed within the standard first‐quantized framework, with special attention to its manner of correspondence to the standard antisymmetrized space‐spin (ASspin) formulation. Second, within this first‐quantized framework, note is made of some “discrepancies” in the correspondence, for example, regarding mismatches of symmetry‐related degeneracies. Third, a novel second‐quantized spin‐free formulation is introduced to overcome these “discrepancies,” and so achieve a one‐to‐one correspondence between ASspin wave functions and second‐quantized spin‐free wave functions. Yet further, this second‐quantized spin‐free description enables the identification of electrons as “para‐Fermions,” at least in the nonrelativistic limit of spin‐free interactions. From the point of view of elementary particle physics, a rather complete picture of the behavior of para‐Fermions emerges with electrons as a proxy, and so suggests that in fact para‐Fermions would be difficult to distinguish from ordinary Fermions, at least in this nonrelativistic limit or with but few such particles. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Peng Dai

String theory uses the first-quantized method (quantum mechanics) to derive scattering amplitudes. External states are considered as vertex operators inserted on the worldsheet generated by an internal string and the amplitudes are calculated perturbatively by calculating vacuum expectation values (vevs) of these vertex operators on worldsheets with different topologies. This approach is different from the common approach of particle theories in which the second-quantized method quantum field theory) is adopted to calculate amplitudes. A natural question to ask is whether there exists a first-quantization formalism for particles that gives particle amplitudes to all orders. This thesis presents the recent research in answering this question. In the first-quantized approach for particles, amplitudes are considered as the vevs of vertex operators inserted on different graphs generated by an internal particle. I refer to these graphs as world-graphs and first-quantized approach for particles as worldgraph approach. To evaluate these vevs, vertex operators for several external states and Green functions on different worldgraphs are needed. In this thesis, various vertex operators are considered and a general method to obtain scalar Green functions on different worldgraphs is obtained. Some examples of the worldgraph approach to amplitudes in scalar theory and Yang-Mills theory are presented.

John Cardy

Hrvoje Nikolić

The relativistic effects of the integer-spin quantum field theory imply that the wave functions describing a fixed number of particles do not admit the usual probabilistic interpretation. Among several most popular interpretations of quantum mechanics applied to first quantization, the only interpretation for which this fact does not lead to a serious problem, and therefore the only consistent interpretation of first quantization, is the de Broglie-Bohm interpretation.