Spinors Extras SymbolSee Also »|More About »

LvBA

LvBA[b, a]
represents vector composed of two independent massless or massive spinors labeled by b and a: .
  • If at least one of spinors is massless than LvBA[b, a] is also massless.
EXAMPLESCLOSE ALL
Properties & Relations   (15)
With activated notation LvBA[b, a], with b and a being massless or massive spinors, is denoted by
:
When at least one of arguments is neither massive nor massless spinor LvBA[b, a] notation is not changed:
When spinors in LvBA are the same LvBA[a, a] label is replaced by it's argument label:
When spinors in LvBA are different LvBA[b, a] label is left unchanged:
When arguments of LvBA are the same but don't represent neither massive nor massless spinor LvBA[b, a] label is left unchanged:
When one of arguments of LvBA is massless spinor and the other is massive, massive spinor is automatically replaced by proper massless associated spinor (SpAssoc):
LvBAs are replaced by combinations of argument spinors inside Minkowski products and s invariants:
Massless LvBAs are replaced by combinations of argument spinors inside spinor chains and slashed matrices:
In label representation:
In 2-dim representation:
In 4-dim representation:
LvBA[b, a] is interpreted as LVector when b and a are massless or massive spinors:
When at least one of arguments is neither massive nor massless spinor LvBA[b, a] is not interpreted as LVector:
LvBA[b, a] is interpreted as massless Spinor when b and a are spinors and at least one of them is massless:
When none of arguments is massless spinor LvBA[b, a] is not interpreted as massless Spinor:
When at least one of arguments is neither massive nor massless spinor LvBA[b, a] is not interpreted as massless Spinor:
Default LVector numerical components for LvBA[b, a], with b and a being massless or massive spinors with declared numerical components, can be declared by using DeclareLVectorMomentum with one argument (this will also automatically set default numerical values for needed SpAssoc and SpRef if it they were not set earlier):
Numerical values obtained this way are equal to proper combinations of numerical values for b and a spinors:
When DeclareLVectorMomentum, with LvBA[b, a] as only argument, is called when some of needed numerical components are not declared, declaration fails and a warning message is printed:
Default spinor numerical components for LvBA[b, a], with b and a being massless Spinors with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument:
Numerical values obtained this way are equal to proper combinations of numerical values for b and a spinors:
When DeclareSpinorMomentum, with LvBA[b, a] as only argument, is called when b or a does not have declared numerical components declaration fails and a warning message is printed:
Notation   (2)
With activated notation LvBA[b, a], with b and a being massless or massive spinors, is denoted by
:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
Out[3]=
 
When at least one of arguments is neither massive nor massless spinor LvBA[b, a] notation is not changed:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
Out[3]=
Out[3]=
Out[3]=
Out[3]=
LVector interpretation   (2)
LvBA[b, a] is interpreted as LVector when b and a are massless or massive spinors:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
Out[3]=
Out[3]=
Out[3]=
 
When at least one of arguments is neither massive nor massless spinor LvBA[b, a] is not interpreted as LVector:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
Out[3]=
Out[3]=
Out[3]=
Out[3]=
Spinor interpretation   (3)
LvBA[b, a] is interpreted as massless Spinor when b and a are spinors and at least one of them is massless:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
Out[3]=
Out[3]=
 
When none of arguments is massless spinor LvBA[b, a] is not interpreted as massless Spinor:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
 
When at least one of arguments is neither massive nor massless spinor LvBA[b, a] is not interpreted as massless Spinor:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
Out[3]=
Out[3]=
LVector momentum declaration   (2)
Default LVector numerical components for LvBA[b, a], with b and a being massless or massive spinors with declared numerical components, can be declared by using DeclareLVectorMomentum with one argument (this will also automatically set default numerical values for needed SpAssoc and SpRef if it they were not set earlier):
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Numerical values obtained this way are equal to proper combinations of numerical values for b and a spinors:
In[4]:=
Click for copyable input
Out[4]=
 
When DeclareLVectorMomentum, with LvBA[b, a] as only argument, is called when some of needed numerical components are not declared, declaration fails and a warning message is printed:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
In[5]:=
Click for copyable input
Out[5]=
Massless Spinor momentum declaration   (2)
Default spinor numerical components for LvBA[b, a], with b and a being massless Spinors with declared numerical components, can be declared by using DeclareSpinorMomentum with one argument:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Numerical values obtained this way are equal to proper combinations of numerical values for b and a spinors:
In[4]:=
Click for copyable input
Out[4]=
Out[4]=
Out[4]=
 
When DeclareSpinorMomentum, with LvBA[b, a] as only argument, is called when b or a does not have declared numerical components declaration fails and a warning message is printed:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
In[5]:=
Click for copyable input
Out[5]=