ISSN 0027-1349, Moscow University Physics Bulletin, 2009, Vol. 64, No. 1, pp. 44–47. © Allerton Press, Inc., 2009. Original Russian Text © E.V. Arbuzova, A.E. Lobanov, O.S. Pavlova, 2009, published in Vestnik Moskovskogo Universiteta. Fizika, 2009, No. 1, pp. 42–45. 44 In relativistic quantum mechanics only integrals of motion can be considered as observables [1, 2]. There- fore, upon classification of particle states it is necessary to make a complete set of operators which are integrals of motion, i.e., commute with the wave equation oper- ator. For a free particle, the physical meaning of opera- tors included in any complete set is known. However, the account of interaction of the particle charge or anomalous magnetic moment with external magnetic field strongly complicates the problem of interpretation of operators of the complete set, even if it is found. Let us elucidate this using a simple example. The interaction of a particle charge with an external field is included in relativistic equations by extending the derivative, i.e., the canonical momentum operator p µ = i∂ µ is replaced by p µ – eA µ , where e is the particle charge, and A µ is the four-dimensional external field potential. The operator p µ – eA µ can be interpreted as the kinetic momentum operator for a scalar particle. If a particle with a spin is considered, this interpretation is not valid. For example, for a particle with a spin of 1/2 the effect of kinetic momentum operator  µ on the func- tions from the space of solutions of the Dirac equations should be determined not only by the relation 1 (1) but also the condition (2) where m is the particle mass. It is well known that the operator p µ – eA µ does not satisfy condition (2). Obvi- 1 Quantities with “caps” denote scalar products of Dirac matrices and 4-vectors, ≡ γ µ a µ . aˆ  ˆ m, =  2 m 2 , = ously, the problem becomes even more serious if the anomalous Pauli interaction is considered. In [3] we obtained the solutions to the Dirac–Pauli equation for a neutral particle with an anomalous mag- netic moment in external electromagnetic fields of spe- cial form. These solutions can be represented as a result of the action of some, generally speaking, integral oper- ator on the solutions to the equation for a free particle. If solutions for a free particle are chosen in the form of plane waves, the action of this operator is reduced to multiplication by the matrix function, which depends on some parameter q µ . This parameter satisfies the con- dition q 2 = m 2 , and as a consequence, it can be inter- preted as the particle kinetic momentum in the external field. Later the solutions of this form were generalized to the case of axial particle interaction with a constant vector condensate [4–6]. Note that an interaction of this type can be used for phenomenological description of neutrino propagation in a dense medium consisting of fermions [7]. Of course, the presence of the complete system of solutions allows determining the action of operators of the complete set (the complete set of operators should include, along with the components of kinetic momen- tum, the spin projection operator) on functions of their definition domain. However, in many respects, it is interesting to known the explicit form of these opera- tors. This is especially important if these operators can be determined as pseudodifferential operators. In this work we construct the explicit form of oper- ators of the complete set for a neutral particle with an anomalous magnetic momentum µ 0 in the simplest case when the external field with which the particle interacts is constant and homogeneous. Operators of Observables for a Neutral Particle with Anomalous Magnetic Moment in an Electromagnetic Field E. V. Arbuzova a , A. E. Lobanov b , and O. S. Pavlova b a Dubna International University, Dubna, 141980 Russia e-mail: lobanov@phys.msu.ru b Department of Theoretical Physics, Faculty of Physics, Moscow State University, Moscow, 119991 Russia e-mail: arbuzova@uni-dubna.ru Received March 4, 2008 Abstract—The explicit form of operators of kinetic momenta and spin projection for a neutral particle with an anomalous magnetic moment in constant homogeneous electromagnetic field is found. The possible applica- tions of the obtained results in neutrino physics are considered. Key words: integral of motion, anomalous magnetic moment, external field, neutrino DOI: 10.3103/S0027134909010093