Remarks on Duffin–Kemmer–Petiau theory and gauge invariance

Abstract

Two problems relative to the electromagnetic coupling of Duffin-Kemmer-Petiau (DKP) theory are discussed: the presence of an anomalous term in the Hamiltonian form of the theory and the apparent difference between the Interaction terms in DKP and Klein-Gordon (KG) Lagrangians. For this, we first discuss the behavior of DKP field and its physical components under gauge transformations.From this analysis, we can show that these problems simply do not exist if one correctly analyses the physical components of DKP field.

Quantum dynamics of scalar bosons in a cosmic string background

“…Although the formalisms are equivalent in the case of minimally coupled vector interactions [5][6][7], the DKP formalism enjoys a richness of couplings not capable of being expressed in the KG and Proca theories [8,9]. Recently, there has been increasing interest in the so-called DKP oscillator [10][11][12][13][14][15][16][17][18][19].…”

An effective singular oscillator for Duffin–Kemmer–Petiau particles with a nonminimal vector coupling: a two-fold degeneracy

“…Nevertheless, J 1 for a stationary state, as expressed by (9) and (14), is the same at all points of the X-axis and vanishes for a bound-state solution (because Φ σ vanishes as x → ∞), so we demand that s σ ∈ R and so α σ ≥ α crit . Normalizability of Φ σ also requires s σ > −1/2 and due to the two-fold possibility of values of s σ for α crit < α σ < 3/(8m), it seems that the solution of our problem can not be uniquely determined.…”

Bound states of the Duffin–Kemmer–Petiau equation with a mixed minimal–nonminimal vector cusp potential

“…The onus of equivalence between the formalisms represented an objection to the DKP theory for a long time and only recently it was shown that they yield the same results in the case of minimally coupled vector interactions, on the condition that one correctly interprets the components of the DKP spinor [5]- [6]. However, the equivalence between the DKP and the Proca formalisms has already a precedent [7].…”