The Lagrangian formalism of the theory of spin 2 fields

Bhargava, S. C.; Watanabe, H.

doi:10.1016/0029-5582(66)90555-4

Cited by 29 publications

(18 citation statements)

References 11 publications

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“…A wave equation, second order in the first derivatives of the wave function is obtained which implies all the usual subsidiary conditions for spin-2, including the symmetry and tracelessness oftp u~, and, in virtue of these, reduced to the Klein-Gordan equation. The results obtained agree with those of Bhargava and Watanabe [14]. These authors obtained their results by a different, somewhat tentative, method and with the aid of a correct but unproven assumption which we did not have to make.…”

Section: Introductionsupporting

confidence: 81%

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Tensor formulation of spin-1 and spin-2 fields

Macfarlane

Tait

1972

Commun.Math. Phys.

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Section: Introductionsupporting

confidence: 81%

“…It was shown by Bhargava and Watanabe [14] that it is possible to construct an Euler-Lagrange equation for a massive spin-2 field in which the symmetry and the tracelessness of the tensor field employed were not assumed at the outset (cf. also Nath [16]), but emerge finally from this equation.…”

Section: Spin-2 Wave Equationmentioning

confidence: 99%

Tensor formulation of spin-1 and spin-2 fields

Macfarlane

Tait

1972

Commun.Math. Phys.

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“…They confirm the results of Refs. [14][15][16] regarding the existence of other ghost-free second-order models different from the FP theory, contrary to early works [9][10][11][12][13].…”

Section: Discussionmentioning

confidence: 70%

“…The general case of a second-order (in derivatives) Lagrangian for an arbitrary rank-2 tensor e has been investigated in the past in Refs. [9][10][11][12][13]. They concluded that the massive FP theory is the only possibility which avoids ghosts.…”

Section: Introductionmentioning

confidence: 99%

Note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

Dalmazi

2013

Phys. Rev. D

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It is possible to show that there are three independent families of models describing a massive spin-2 particle via a rank-2 tensor. One of them contains the massive Fierz-Pauli model, the only case described by a symmetric tensor. The three families have different local symmetries in the massless limit and can not be interconnected by any local field redefinition. We show here, however, that they can be related with the help of a decoupled and nondynamic (spectator) field. The spectator field may be either an antisymmetric tensor B ¼ ÀB , a vector A or a scalar field ', corresponding to each of the three families. The addition of the extra field allows us to formulate master actions which interpolate between the symmetric Fierz-Pauli theory and the other models. We argue that massive gravity models based on the Fierz-Pauli theory are not expected to be equivalent to possible local self-interacting theories built up on top of the two new families of massive spin-2 models. The approach used here may be useful to investigate dual (nonsymmetric) formulations of higher-spin particles.

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“…where T(Zv)=T{,pv)-(1/4)otlVT{tA)' If SU(2) (j<)SU(2) were an exact symmetry, we would have ,d(+)1" =,d(+)TS. Writing the general structure2 ) ,d~t~~ (q) -,d~t~~~ (q) =F(q2) 0,.0 tlV+G(q2) (o,tl0,v+o'Vo,tl) + H(q2) (o,.qtlqv+o"vq,q.)…”

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confidence: 99%

Relations between the Spectra of 2⁺and 2^-Mesons

Itoh

1968

Prog. Theor. Phys.

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Current algebra imposes satisfactory relations between the spectra of the 1 + and 1mesons.!) If chiral SUeZ) &;;SU(Z) were an exact symmetry, we may expect the A2 (JPG=Z+ -) meson to be accompanied with an 1=1, JPG=Z-+ meson of the same mass, we call it the A 25 meson. We will give relations between the spectral functions of the symmetric tensor current Tf",u) and symmetric axial-tensor current T~~ul> which couple to the Z+ and Z-mesons, respectively, where Tf",,) = (l/Z) (T~u+TC;}.), and the baryon part of T~u is given as follows, T~~,) and T~";' are given by replacing r Ii in Eq. (1) with r"r5' Let us begin with a free Hamiltonian (Z) where H oo is the invariant part under SU (Z) &;;SU (Z), and ,1,uo, which corresponds to the baryon mass term, is noninvariant.We define the operators pua and Pc";,) as follows,and similarly pu5a and Pi'u). By commuting pu5a with uo, we get bu 5a which is proportional.to (l/Z) (?itar50vif;-oijjrar5if;): t). (4)The divergence of the axial tensor current can be expressed in terms of this commutator:o"T~~=i[p}a, ,1,uoJ =Z,1,bv 5a , o"T~~,)=,1,bv5a, o"T't",,) =0 .(5) bV 5a is a sort of effective meson operator, which has 1=1, JPG=I++,and a possible candidate for such a meson is B(lZ10). To illustrate the commutation relations of Pc";,) and Pf;'j with interactions, we introduce a simple model:where B" is a neutral vector meson field.We also replace 0" in T;, and T~~ with O"-iEB,,, Then divergences of the currents are given by o"T(~u)=iEfvijjr"raif;,o "Ti':,) =iEfv,,?ir "r5raif;+ J..bv 5a -iElBv?ir 5 r a if;,where fv "=ovB,,-o,,Bv' Ttl") and Tt:u) have no Bet meson terms because of the absence of isotopic spin of the meson. We note that both sides of Eq. (7) and the double divergence o"ovT{,,,,u) have odd G parity, and o"ovTt;,) has even G parity.We consider the following vacuum ex-at East Tennessee State University on May 31, 2015 http://ptp.oxfordjournals.org/ Downloaded from

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The Lagrangian formalism of the theory of spin 2 fields

Cited by 29 publications

References 11 publications

Tensor formulation of spin-1 and spin-2 fields

Tensor formulation of spin-1 and spin-2 fields

Note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

Relations between the Spectra of 2⁺and 2^-Mesons

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The Lagrangian formalism of the theory of spin 2 fields

Cited by 29 publications

References 11 publications

Tensor formulation of spin-1 and spin-2 fields

Tensor formulation of spin-1 and spin-2 fields

Note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

Relations between the Spectra of 2+and 2-Mesons

Contact Info

Product

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Relations between the Spectra of 2⁺and 2^-Mesons