JHEP07(2018)133
system containing the invariant functional. Then, in section 3 we address a problem of
covariantization of the extended HS equations. To do that we discuss a generalization of
the deformed oscillator algebra in section 3.2. A manifestly covariant form of HS equations
is given in section 3.3. Finally, in section 4 we elaborate a covariant perturbation theory
for the obtained equations. Brief conclusions are in section 5.
2 Lorentz covariant HS equations
Let us start by reviewing the HS equations in four dimensions of [2] (see also [5]) and their
Lorentz covariantization. The equations have the following standard form
dW + W ∗ W = iθ
A
θ
A
+ iηB ∗ γ + i¯ηB ∗ ¯γ , (2.1)
dB + [W, B]
∗
= 0 , (2.2)
where W(Z, Y ; K|x) is the 1-form in the double graded space spanned by anticommuting
dx
m
and auxiliary θ
A
differentials. W contains HS potentials with all their descendants in
space-time subsector W and the compensator-like field S in the θ-subsector,
W(Z, Y ; K|x) = W
m
(Z, Y ; K|x)dx
m
+ S
A
(Z, Y ; K|x)θ
A
, (2.3)
{dx
m
, dx
n
} = {dx
m
, θ
A
} = {θ
A
, θ
B
} = 0 . (2.4)
Space-time indices m, n as well as Majorana spinor fiber indices A, B range four values.
B(Z, Y ; K|x) is a 0-form master field, containing lower spin matter fields and HS curvatures.
Apart from x-dependence, W and B depend on a number of generating variables.
Commuting twistor-like variables Y
A
= (y
α
, ¯y
˙α
) and Z
A
= (z
α
, ¯z
˙α
) are designed to pack
up HS fields and auxiliary fields, where spinor indices α, β, . . . range two values. The
associative star-product operation acts on functions f(Z, Y )
(f ∗ g)(Z, Y ) =
1
(2π)
4
Z
dUdV f (Z + U, Y + U)g(Z − V, Y + V )e
iU
A
V
A
, (2.5)
where U
A
V
A
:= U
A
V
B
AB
with some sp(4)-invariant symplectic form
AB
= −
BA
. Indices
are raised and lowered with the aid of
AB
as follows, X
A
=
AB
X
B
and X
A
=
BA
X
B
.
The star product can be seen to induce the following commutation relations
[Y
A
, Y
B
]
∗
= −[Z
A
, Z
B
]
∗
= 2i
AB
, [Y
A
, Z
B
]
∗
= 0 . (2.6)
It admits the inner Klein operators
κ = e
iz
α
y
α
, ¯κ = e
i¯z
˙α
¯y
˙α
. (2.7)
Their characteristic properties are
{κ, y
α
}
∗
= {κ, z
α
}
∗
= 0 , κ ∗ κ = 1 , (2.8)
analogously in the antiholomorphic sector for ¯κ.
– 4 –
剩余22页未读，继续阅读
weixin_38559346
- 粉丝: 4
- 资源: 943
我的内容管理
展开
最新资源
- AirKiss技术详解：无线传递信息与智能家居连接
- Hibernate主键生成策略详解
- 操作系统实验：位示图法管理磁盘空闲空间
- JSON详解：数据交换的主流格式
- Win7安装Ubuntu双系统详细指南
- FPGA内部结构与工作原理探索
- 信用评分模型解析：WOE、IV与ROC
- 使用LVS+Keepalived构建高可用负载均衡集群
- 微信小程序驱动餐饮与服装业创新转型：便捷管理与低成本优势
- 机器学习入门指南：从基础到进阶
- 解决Win7 IIS配置错误500.22与0x80070032
- SQL-DFS：优化HDFS小文件存储的解决方案
- Hadoop、Hbase、Spark环境部署与主机配置详解
- Kisso：加密会话Cookie实现的单点登录SSO
- OpenCV读取与拼接多幅图像教程
- QT实战：轻松生成与解析JSON数据
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
