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Some reference papers A. Bashir, Ma . de Jesus Anguiano Galicia Fermions in odd space-time dimensions: back to basics Few-Body Systems 0, 1–8 (2008 ), hep-ph /0502089v1 C. Burden, A. N. Burkitt Lattice Fermions in Odd Dimensions Europhys. Lett., 3 (5), pp. 545-552 (1987 )

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fermions in odd dimensions

Some reference papers

A. Bashir, Ma. de Jesus Anguiano Galicia

Fermions in odd space-time dimensions: back to basics

Few-Body Systems 0, 1–8 (2008),hep-ph/0502089v1

C. Burden, A. N. Burkitt

Lattice Fermions in Odd Dimensions

Europhys. Lett., 3 (5), pp. 545-552 (1987)

W. Bietenholz, J, Nishimura

Ginsparg-Wilson fermions in odd dimensions

JHEP07(2001)015, hep-lat/0012020v2

Y. Kikukawa, H. Neuberger

Overlap in odd dimensions

Nucl. Phys. B, 513-3 (1998) 735, hep-lat/9707016v1

Fermions in odd dimensions

slide2

In odd dimensions the Clifford algebra does not admit a , so chiral symmetry cannot be defined

Two inequivalent representation of the algebra exist

Parity anomaly

C. Burden, A. N. Burkitt

Lattice Fermions in Odd Dimensions

Europhys. Lett., 3 (5), pp. 545-552 (1987)

Starting from staggered formulation, analogous to the 4d case, shows that its continuum equivalent are flavors of components spinors.

Parity symmetry is recovered by using both representations

A set of chiral symmetries can be defined.

slide3

A. Bashir, Ma. de Jesus Anguiano Galicia

Fermions in odd space-time dimensions: back to basics

Few-Body Systems 0, 1–8 (2008), hep-ph/0502089v1

They show that it is possible to write a formulation of odd dimensional fermions using the fundamental representation of the Clifford algebra.

The massless action has more symmetry than the massive case.

“We demonstrate that by taking into account both the inequivalent fundamental representations of the gamma matrices for odd number of space-time dimensions, the resulting Lagrangian is not only parity invariant but also that we can write out chiral transformations within the two-component description of the fermion spinors which mix the fields belonging to the different inequivalent representations.”

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