Calculating trace with slashed item

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In summary, the task at hand is to find Tr q (p + m) q (p + m), and the relevant equation is Tr p q = 4pq. However, since q p q and similar terms are not square matrices, the trace has no meaning. Treating (p + m) as a covariant vector may help, but it will result in a messy equation with many q and p terms. The clarification that p is not a vector allows for the trace to make sense.
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qaok
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Homework Statement



I was asked to find Tr [STRIKE]q[/STRIKE] ([STRIKE]p[/STRIKE] + m) [STRIKE]q[/STRIKE] ([STRIKE]p[/STRIKE] + m)

Homework Equations



Tr [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] = 4pq

The Attempt at a Solution



If I expand it as Tr ([STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] + m [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] + m [STRIKE]q[/STRIKE] [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] + (m^2)([STRIKE]q[/STRIKE])^2 ), although Tr Π(odd number of gamma matrices) = 0, since [STRIKE]q[/STRIKE] [STRIKE]p[/STRIKE] [STRIKE]q[/STRIKE] and similar terms are not square matrices, trace has no meaning. If I treat ([STRIKE]p[/STRIKE] + m) as a covariant vector (adding m to each component of [STRIKE]p[/STRIKE], I can get a scalar*I, but a lot of [STRIKE]q[/STRIKE]_0,1,2,3 [STRIKE]p[/STRIKE]_0,1,2,3 terms will come out and get really messy. Can anyone help me please? Thank you.
 
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  • #2
I thought [STRIKE]p[/STRIKE] was a vector, but now I realize that it is not. So the trace makes sense.
 

1. What is the purpose of calculating trace with slashed item?

The purpose of calculating trace with slashed item is to determine the amount of a certain substance or element present in a sample or solution. This can be useful in various scientific fields such as chemistry, biology, and environmental science.

2. What is the formula for calculating trace with slashed item?

The formula for calculating trace with slashed item is: Trace = (Concentration of Sample / Concentration of Standard) x Amount of Standard Used. This formula is also known as the dilution factor method.

3. What is the difference between trace analysis and standard analysis?

Trace analysis refers to the measurement and detection of small amounts of a substance in a sample, while standard analysis is used to determine the concentration of a substance in a sample by comparing it to a known standard. Trace analysis is typically used for substances present in very low concentrations, while standard analysis is used for higher concentrations.

4. How do you determine the concentration of a sample using trace analysis?

To determine the concentration of a sample using trace analysis, you would need to first measure the amount of the substance present in the sample using a suitable analytical method. This measurement is then compared to a known standard with a known concentration to calculate the concentration of the sample.

5. What are the limitations of calculating trace with slashed item?

There are a few limitations to calculating trace with slashed item, such as the potential for errors in measurement or inaccuracy of the standard used. Additionally, certain substances may be difficult to detect or measure accurately at very low concentrations. It is important to use proper techniques and equipment to minimize these limitations and ensure accurate results.

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