We investigate some peculiar aspects of the so called Lee-Wick Electrodynamics focusing on physical effects produced by the presence of sources for the vector field. The interactions between stationary charges distributions along parallel branes with arbitrary dimensions is investigated and the energy of a point charge is discussed. Some physical phenomena produced in the vicinity of a Dirac string are also investigated. We consider the Lee-Wick theory for the scalar field, where it can emerge some interesting effects with no counterpart for the vector gauge field theory. *
Lee-Wick electrodynamics in the vicinity of a conducting plate is investigated. The propagator for the gauge field is calculated and the interaction between the plate and a point-like electric charge is computed. The boundary condition imposed on the vector field is taken to be the one that makes, on the plate, the normal component of the dual field strength to the plate vanish. It is shown that the image method is not valid in Lee-Wick electrodynamics.
In this paper we study the ultraviolet and infrared behavior of the self-energy of a pointlike charge in the vector and scalar Lee-Wick electrodynamics in a d + 1 dimensional space time. It is shown that in the vector case, the self-energy is strictly ultraviolet finite up to <7 = 3 spatial dimensions, finite in the renormalized sense for any d odd, infrared divergent for <7 = 2, and ultraviolet divergent for <7 > 2 even. On the other hand, in the scalar case, the self-energy is striclty finite for d < 3, and finite, in the renormalized sense, for any d odd.One of the most remarkable features of the so-called LeeWick electrodynamics is the fact that this theory leads to a finite self-energy for a pointlike charge in 3 + 1 dimensions [1][2][3][4][5], what has important implications in the quantum context, mainly in what concerns the renormalizability of the theory [6,7]. Theories of superior derivatives for the scalar field have been also considered in the literature, mainly after the proposal of the so-called Lee-Wick Standard Model (LWSM) [8][9][10][11][12][13][14][15][16][17][18][19][20].Among other subjects concerning Lee-Wick electrody namics, in the work of Ref.[21] the self-energy of a pointlike charge in an arbitrary number of spatial dimen sions was discussed. The presented results were specula tive, not conclusive, and indicated that the pointlike particle self-energy is divergent for space dimensions higher than 3. That is an important subject in the context of theories with higher dimensions, in what concerns models with superior derivatives, because some well-known results of Lee-Wick theories, which are valid in 3 + 1 dimensions, are no longer applicable when the space has not 3 dime dimensions.In this paper we show that, by using dimensional regularization, the self-energy of a pointlike particle is finite when the space has an odd dimension and diverges when the space has an even dimension. We also consider the self-energy of a pointlike source for the Klein-GordonLee-Wick field, where there are two mass parameters involved.Let us start with the Lee-Wick electrodynamics. It is described by the Lagrangian density [4,5] C a = . _ p mv . ^1where .F is the vector external source, F^v =( 2)is the field strength, A1 * is the vector potential, and m is a parameter with mass dimension. The third term on the right-hand side of (1) was introduced in order to fix the gauge and £, is a gauge fixing parameter. The correspondingpropagator is [21] ( 3)The energy of the system due to the presence of the source is given by [21-23] Ea = lim -L [ dd+lxdd+xy J^x )D^(x ,y )J v{y). (4)T-*oo 1 1 J Now we take the source of a pointlike stationary charge A placed at position a in a d + 1 space-timewhere < 5 is the Dirac delta function in <7 dimensions.Replacing the above expression in Eq. (4) and perform ing the integrals in x°, p°, and y°, we have * / ddp "1 1 {2n)d p2 p2 + m2 A2m2 f dd p 1 J ( 2n)dP2(p2 -m 2) 1550-7998/2015/91(2)/027701 (4) 027701-1
The aim of this work is to discuss some aspects of the reduction of order formalism in the context of the Fadeev-Jackiw symplectic formalism, both at the classical and the quantum level. We start by reviewing the symplectic analysis in a regular theory (a higher derivative massless scalar theory), both using the Ostrogradsky prescription and also by reducing the order of the Lagrangian with an auxiliary field, showing the equivalence of these two approaches. The interpretation of the degrees of freedom is discussed in some detail. Finally, we perform the similar analysis in a singular higher derivative gauge theory (the Podolsky electrodynamics), in the reduced order formalism: we claim that this approach have the advantage of clearly separating the symplectic structure of the model into a Maxwell and a Proca (ghost) sector, thus complementing the understanding of the degrees of freedom of the theory and simplifying calculations involving matrices.
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