Tachyon

Energy

When we particles particles, the <action (physics)> is obtained by integrating the <Lagrangian> over time:
$$
Action = \int_{t_0}^{t} L(x(t), \pdv{x(t)}{t}, t) dt
$$

In the case of <field (mathematics)> however, we can expand the Lagrangian out further, to also integrate over the space coordinates and their derivatives.

Since we are now working with something that gets integrated over space to obtain the total action, much like <density> would be integrated over space to obtain a total mass, the name "Lagrangian density" is fitting.

E.g. for a 2-dimensional field $f(x, y, t)$:
$$
Action = \int_{t_0}^{t} L(f(x, y, t), \pdv{f(x, y, t)}{x}, \pdv{f(x, y, t)}{y}, \pdv{f(x, y, t)}{t}, x, y, t) dx dy dt
$$

Of course, if we were to write it like that all the time we would go mad, so we can just write a much more condensed <vectorized> version using the <gradient> with $x \in \R^2$:
$$
Action = \int_{t_0}^{t} L(f(x, t), \grad{f(x, t)}, x, t) dx dt
$$

And in the context of <special relativity>, people condense that even further by adding $t$ to the spacetime <Four-vector> as well, so you don't even need to write that separate pesky $t$.

The main point of talking about the Lagrangian density instead of a Lagrangian for fields is likely that it treats space and time in a more uniform way, which is a basic requirement of <special relativity>: we have to be able to mix them up somehow to do <Lorentz transformations>. Notably, this is a key ingredient in a/the formulation of <quantum field theory>.


Lagrangian density

{c}

https://github.com/CIDARLAB/cello

Design software for <synthetic biological circuit>{parent}.

The input is in <Verilog>! Overkill?

Then it essentially maps to a <standard cell library> of biological primitives!


CIDARLAB/cello

{title2=Mammals + extinct reptile like cousins}
{wiki}

<Mammals> and a bunch of <extinct> animals that look more like mammals than <reptiles>.

TODO name: Wikipedia says "being with a fused arch" but what does that mean???


Synapsid

{c}
{tag=1973 Nobel Prize in Physics}
{wiki}


Brian Josephson

Nuclear weapon test

Activation energy

Software testing

Chinese television drama

{c}
{wiki}

* https://www.youtube.com/@stevensimon2285


Steven H. Simon

{c}
{wiki}

= Country of the United Kingdom
{synonym}


Countries of the United Kingdom

{disambiguate=United States}

= Democrat
{synonym}
{title2}


Democratic Party

Tests of general relativity

{disambiguate=physics}
{wiki}

= Quantized
{disambiguate=physics}
{synonym}

<Quantum field theory lecture by Tobias Osborne (2017)> mentions that quantization is a guess.


Title	Author	Created	Updated
Tachyon	Ciro Santilli 32	1970-01-01	1970-01-01
Energy	Ciro Santilli 32	1970-01-01	1970-01-01
Lagrangian density	Ciro Santilli 32	1970-01-01	1970-01-01
CIDARLAB/cello	Ciro Santilli 32	1970-01-01	1970-01-01
Synapsid	Ciro Santilli 32	1970-01-01	1970-01-01
Brian Josephson	Ciro Santilli 32	1970-01-01	1970-01-01
Nuclear weapon test	Ciro Santilli 32	1970-01-01	1970-01-01
Activation energy	Ciro Santilli 32	1970-01-01	1970-01-01
Software testing	Ciro Santilli 32	1970-01-01	1970-01-01
Chinese television drama	Ciro Santilli 32	1970-01-01	1970-01-01
Steven H. Simon	Ciro Santilli 32	1970-01-01	1970-01-01
Countries of the United Kingdom	Ciro Santilli 32	1970-01-01	1970-01-01
Democratic Party	Ciro Santilli 32	1970-01-01	1970-01-01
Tests of general relativity	Ciro Santilli 32	1970-01-01	1970-01-01
Quantization	Ciro Santilli 32	1970-01-01	1970-01-01
Hall effect sensor	Ciro Santilli 32	1970-01-01	1970-01-01
Parody religion	Ciro Santilli 32	1970-01-01	1970-01-01
Magnetic dipole moment	Ciro Santilli 32	1970-01-01	1970-01-01
Feijoada	Ciro Santilli 32	1970-01-01	1970-01-01
Chocolate	Ciro Santilli 32	1970-01-01	1970-01-01

Ciro Santilli (@cirosantilli, 32)