论文标题
$κ$ noncommutative量子场理论的新型平面波理论
New class of plane waves for $κ$-noncommutative Quantum Field Theory
论文作者
论文摘要
我们讨论了$κ$ -Minkowski非交通时空的自由标量量子场理论的构建。我们这样做的是$κ$-Poincaré-invariant $ n $ - 点函数，即尊重时空的变形对称性的多局部函数。如我们中一些人的上一篇论文所示，只有换向关系的光明版本，这才允许构建$ n $ n $点的协变量代数，该代数概括了$κ$ -Minkwosski的通勤关系。我们解决了先前方法的主要缺点，这阻止了完全协变量的量子场理论的发展：动量空间的非Lorentz-Invariant边界的出现。 To solve this issue, we propose to ``extend" momentum space by introducing a class of new Fourier modes and we prove that this approach leads to a consistent definition of the Pauli-Jordan function, which turns out to be undeformed with respect to the commutative case. We finally address the quantization of our scalar field and obtain a deformed, $κ$-Poincaré-invariant, version of the bosonic oscillator代数。
We discuss the construction of a free scalar quantum field theory on $κ$-Minkowski noncommutative spacetime. We do so in terms of $κ$-Poincaré-invariant $N$-point functions, i.e. multilocal functions which respect the deformed symmetries of the spacetime. As shown in a previous paper by some of us, this is only possible for a lightlike version of the commutation relations, which allow the construction of a covariant algebra of $N$ points that generalizes the $κ$-Minkowski commutation relations. We solve the main shortcoming of our previous approach, which prevented the development of a fully covariant quantum field theory: the emergence of a non-Lorentz-invariant boundary of momentum space. To solve this issue, we propose to ``extend" momentum space by introducing a class of new Fourier modes and we prove that this approach leads to a consistent definition of the Pauli-Jordan function, which turns out to be undeformed with respect to the commutative case. We finally address the quantization of our scalar field and obtain a deformed, $κ$-Poincaré-invariant, version of the bosonic oscillator algebra.
