Here, [zeta] acquires a nonminimal kinetic term of the form [omega]([phi]) due to its interaction with [phi]([phi], [zeta] can be identified with the scalar dilaton field and the

pseudoscalar axion field, respectively), while *[F.sup.[mu]v] = (1/2)[[epsilon].sup.[mu]v[kappa][lambda]][F.sub.[kappa][lambda]] is the Hodge-dual Maxwell field strength.

where [I.sub.AB] denotes the

pseudoscalar forming the minimal subspace which contains A and B.

[38], electro-weak radiative corrections to scalar,

pseudoscalar, and tensor interactions of any origin induce contributions to P,T-violating e - q interactions.

Roy, "Darboux partners of

pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials," Annals of Physics, vol.

Here, i is a

pseudoscalar in geometric algebra of three dimensions [40], it commutes with all elements of the algebra and [i.sup.2] = -1.

1:00 PROBING LIGHT

PSEUDOSCALAR, AXIAL VECTOR STATES THROUGH [[eta].sub.b] [right arrow] [[tau].sup.+] [[tau].sup.-]

Equation (2.5) demonstrates that a P-odd T-odd interaction does modify, as claimed in [6], the energy dependence of the P-odd asymmetry associated with the

pseudoscalar [sigma] * [n.sub.[gamma]].

where the superscripts i and j refer to four operators in the effective Lagrangian given by (4) (the tensors related to the scalar and

pseudoscalar operators can be understood through the relations given by (21) and (22)); in the SM, i = j corresponds to the operator [bar.p][[gamma].sub.[mu]] (1 - [[gamma].sub.5])b[bar.l][[gamma].sup.[mu]](1 - [[gamma].sub.5])[nu].

(The possibility of using a

pseudoscalar factor is not discussed here because this work aims to examine the parity conserving electromagnetic interactions of a quantum mechanical particle.) It is shown below how these two requirements impose dramatic constraints on acceptable quantum mechanical equations of motion of a charged particle.

Here [psi] is a Majorana spinor field, S is a scalar field, and P is a

pseudoscalar field.

where E, p, m, t and r are respectively energy, momentum, mass, time, space and the symbols [+ or -]1, [+ or -]i, [+ or -]i, [+ or -]j, [+ or -]k, [+ or -]i, [+ or -]j, [+ or -]k are used to represent the respective units required by the scalar,

pseudoscalar, quaternion and multivariate vector groups.