9.11 Fermi Particles
222
GAUGE FIELDS AND STRINGS
There exists a beautiful extension of the bosonic string, the NeveuSchwarz-Ramond string (NSR) which represents a string analogue of
Dirac particles. We will start this section by describing the path integral
representation for these particles and then generalize it to the string
case.
Fermions can be described in many different ways. One of them, from
which we start, is to replace an ordinary path
= x^(i) by a super
“surface”. Namely to consider a function
6) = x^{t) +
e^ = o
(9.313)
(9.314)
The superspace (i, 9) possesses the symmetry:
dj = 80
3^9 = 8,
= 0; 80 98 = 0
The commutator of two such transformations is an ordinary shift in t :
We can define a covariant derivative ^ by:
d
d
/ d
d
— - 8Ì ~ + 0
(9.315)
30 ^ dt \d9
d
d
^ = ^ + 9 -
30
3t
= -:r 3t
The supercovariant action is given by:
5 = i jd i d0
3t
(9.316)
(9.317)
222
GAUGE FIELDS AND STRINGS
There exists a beautiful extension of the bosonic string, the NeveuSchwarz-Ramond string (NSR) which represents a string analogue of
Dirac particles. We will start this section by describing the path integral
representation for these particles and then generalize it to the string
case.
Fermions can be described in many different ways. One of them, from
which we start, is to replace an ordinary path
= x^(i) by a super
“surface”. Namely to consider a function
6) = x^{t) +
e^ = o
(9.313)
(9.314)
The superspace (i, 9) possesses the symmetry:
dj = 80
3^9 = 8,
= 0; 80 98 = 0
The commutator of two such transformations is an ordinary shift in t :
We can define a covariant derivative ^ by:
d
d
/ d
d
— - 8Ì ~ + 0
(9.315)
30 ^ dt \d9
d
d
^ = ^ + 9 -
30
3t
= -:r 3t
The supercovariant action is given by:
5 = i jd i d0
3t
(9.316)
(9.317)